Advances in Ergodic Theory, Hyperbolic Dynamics and Statistical Laws the Australian National University 28 November – 2 December 2016

Advances in Ergodic Theory, Hyperbolic Dynamics and Statistical Laws The Australian National University 28 November – 2 December 2016

Sponsors MATHSFEST Program 28 November – 2 December 2016

Time Monday Tuesday Wednesday Thursday Friday

Registration 8:30

Invited Lecture Invited Lecture Invited Lecture Invited Lecture Invited Lecture 9:00 F. Ledrappier D. Kelly C. Liverani F. Pene` K. Ramanan Coffee Break Coffee Break Coffee Break Coffee Break Coffee Break 10:00 T. Dooley Invited Lecture Invited Lecture Invited Lecture Invited Lecture 10:30 B. Goldys M. Dellnitz M. Pollicott K. Burns A. Blumenthal 11:00 S. Balasuriya J. Wouters K. Yamamoto V. Climenhaga A. Sims 11:30 P. Koltai C. Kalle I. Rios J. F. Alves E. G. Altmann 12:00 Lunch Lunch Lunch Lunch Lunch 12:30

Invited Lecture Invited Lecture Invited Lecture 14:00 A. Hassell M. J. Paciﬁco A. Wilkinson Coffee Break Coffee Break Coffee Break 15:00 D. Dragiceviˇ c´ S. Hittmeyer T. Schindler 15:30 H. Osinga S. V. da Silva M. Field 16:00 M. Nicol 16:30 K. Burns event 17:00 Posters/Drinks/BBQ 18:00 Practical Information

Venue Welcome to the Math(s)Fest! The talks for the Advances in Ergodic Theory, Hyperbolic Dynamics and Statistical Laws Workshop will all be held in the main hall of University House on the ANU campus. This booklet includes a map of campus and University House is in the top right corner of square C2. Events On Monday evening from 18:00 to 22:00, the workshop is hosting a welcome barbeque and poster session at University House. If you would like to bring an extra guest to the barbeque, please let us know as soon as possible. The cost per extra guest will be AUD $60. On Thursday evening at 17:00, the workshop is celebrating the Keith Burns’ sixtieth birthday in the Common Room of University House. Light snacks and, of course, cake will be served. There will also be a cash bar. Free Afternoons No talks are scheduled for Wednesday and Friday afternoons and there are a number of attractions near the ANU campus. The National Museum of Australia is just south of campus and in easy walking distance. Further south, on the other side of the river, are the National Gallery of Australia and the Old and New Parliament Buildings. We plan to put more information up on the workshop website. There is also a tourist bus line (Route 81/981) and a free city loop bus (Route 101). Internet Eduroam is available throughout the ANU campus. If you cannot access the internet through Eduroam, talk to one of the organisers to get access to the wi-ﬁ at University House. Accommodation If the workshop has arranged your accommodation, then you should have received an email from us with details. If you unsure of your check-in details, please talk to one of the organizers or contact us at [email protected]. Dining There are a number of restaurants on campus, as noted by the fork and knife logos on the campus map. Most of them are in and around Union Court (square C3 on the map). East of the ANU Campus are a number of restaurants in and around the large “Canberra Center” shopping complex. This complex also has a supermarket for buying groceries. This area is about a twenty minute walk from University House.

We hope you have a great time in Canberra!

Organising Committee Gary Froyland Cecilia Gonz´alez-Tokman Georg Gottwald Andy Hammerlindl Matthew Nicol Luchezar Stoyanov

1 List of Registrants

Current as of Thu 10 Nov 2016

Assoc Prof Eduardo G. Altmann University of Sydney Prof JoséF. Alves University of Porto Mr Fadi Antown University of New South Wales Assoc Prof Sanjeeva Balasuriya The University of Adelaide Ms Chantelle Louise Blachut The University of Queensland Dr Alex Blumenthal University of Maryland College Park Prof Keith Burns Northwestern University Mr Timothy Peter Bywaters University of Sydney Prof Vaughn Climenhaga University of Houston Mr Peter Cudmore The University of Queensland Prof Michael Dellnitz University of Paderborn Dr Davor Dragiˇcević University of New South Wales Dr Nazife Erkursun Ozcan Hacettepe University Prof Michael John Field Imperial College London Prof Gary Froyland University of New South Wales Prof Beniamin Goldys University of Sydney Dr Cecilia González-Tokman The University of Queensland Prof Georg Gottwald University of Sydney Mr Richard Greenhalgh The University Of Western Australia Dr Andy Hammerlindl Monash University Prof Andrew Hassell Australian National University Dr Stefanie Hittmeyer The University of Auckland Mr Kieran Jarrett University of Bath Dr Charlene Kalle University of Leiden Dr David Kelly New York University Dr Robert Kenny The University Of Western Australia Mr Alexander Khor The University Of Western Australia Dr PéterKoltai Freie UniversitätBerlin Dr Bernd Krauskopf University of Auckland Mr Eric Kwok University of New South Wales Prof Fran¸coisLedrappier UniversitéParis 6 Prof Carlangelo Liverani Universitàdegli Studi di Roma “Tor Vergata” Mr Michael Arthur Mampusti University of Wollongong Dr Gemma Mason The University of Auckland Ms Fakhereh Mohammad esmaeili fakhereh University of Hyderabad Mr Jack Murdoch Moore The University Of Western Australia Dr Rua Murray University of Canterbury Prof Matthew James Nicol University of Houston Mr Adam Nie Australian National University Mr Daniel Nix Australian National University Prof Hinke Osinga The University of Auckland Dr Maria Jose Pacifico Universidade Federal do Rio de Janeiro Prof Jayantha Pasdunkorale Arachchige University of Ruhuna Prof Fran¸coisePène Universitéde Bretagne Occidentale Prof Mark Pollicott University of Warwick Prof Kavita Ramanan Brown University Prof Isabel Rios Universidade Federal Fluminense Dr Tanja Schindler Australian National University Dr Simone Vasconcelos da Silva Universidade de Bras´ılia

2 List of Registrants

Prof Aidan Sims University of Wollongong Prof Luchezar Stoyanov The University Of Western Australia Dr Melissa Tacy Australian National University Dr Ilknur Tulunay University of Technology, Sydney Dr Petrus van Heijster Queensland University of Technology Prof Amie Wilkinson University of Chicago Mr John Wormell University of Sydney Dr Jeroen Wouters University of Sydney Dr Kenichiro Yamamoto Nagaoka University of Technology Dr Yiwei Zhang Huazhong Univ of science and technology

3 1. Talks

1.1. Sampling Rare Trajectories in Chaotic System hyperbolic trajectory. We establish, using both Eduardo G. Altmann (University of Sydney) theoretical arguments and empirical verification 12:00 Fri 2 December 2016 – from model and experimental data, that the HNs Assoc Prof Eduardo G. Altmann profoundly impact the Lagrangian stretching ex- perienced by fluid elements. In particular, we I will present a general framework to search and show that fluid elements traversing a flow experi- sample rare trajectories in chaotic systems. The ence exponential boosts in stretching while within main result is to show how properties of the sys- these time-varying regions, that greater residence tem (e.g., Lyapunov exponents, fractality) should time within HNs is directly correlated to larger be included in the proposal step of Markov Chain Finite-Time Lyapunov Exponent (FTLE) values, Monte Carlo methods. Results are shown for two and that FTLE diagnostics are reliable only when problems: (i) computing long-lived trajectories in the HNs have a geometrical structure that is reg- transient-chaos problems; and (ii) sampling tra- ular in a specific sense. jectories with atypical chaoticity, as measured by an atypically large or small finite-time Lyapunov 1.4. Lyapunov exponents for small random exponent. We confirm numerically for different perturbations of predominantly hyperbolic classes of (high-dimensional) chaotic systems that two-dimensional volume-preserving our algorithm scales polynomially with the ob- diffeomorphisms, including the Standard Map servable, a dramatic improvement over the ex- Alex Blumenthal (University of Maryland College ponential scaling obtained in traditional uniform- Park) sampling methods. 11:00 Fri 2 December 2016 – 1.2. Gibbs-Markov-Young structures for partially Dr Alex Blumenthal hyperbolic attractors An outstanding problem in smooth ergodic the- JoséF. Alves (University of Porto) ory is the estimation from below of Lyapunov ex- 12:00 Thu 1 December 2016 – ponents for maps which exhibit hyperbolicity on Prof JoséF. Alves a large but non-invariant subset of phase space. It is notoriously difficult to show that Lypaunov Gibbs-Markov-Young structures have been fre- exponents actually reflect the predominant hyper- quently used in last decades as an important tool bolicity in the system, due to cancellations caused for studying the statistical properties of systems by the ’switching’ of stable and unstable directions with some hyperbolicity. In articular, the decay in those parts of phase space where hyperbolicity of correlations and large deviations can be deter- is violated. mined by the tail of recurrence times associated In this talk I will discuss the inherent difficulties of to these structures. In the case of partially hy- the above problem, and will discuss recent results perbolic attractors, some results have appeared when small IID random perturbations are intro- in the literature, depicting the whole scenario in duced at every time-step. In this case, we are able a fairly reasonable way in the mostly expanding to show with relative ease that for a large class of case. The mostly contracting case is still far from volume-preserving predominantly hyperbolic sys- being completely understood. In this talk we will tems in two dimensions, the top Lypaunov expo- present some recent results in both directions. nent actually reflects the predominant hyperbolicity in the system. Our results extend to the 1.3. Hyperbolic neighbourhoods in nonautonomous well-studied Chirikov Standard Map at large cou- flows pling. This work is joint with Lai-Sang Young and Sanjeeva Balasuriya (The University of Adelaide) Jinxin Xue. 11:30 Mon 28 November 2016 – Sanjeeva Balasuriya, Rahul Kalampattel and 1.5. The Weil Petersson geodesic flow Nicholas Ouellette Keith Burns (Northwestern University) Hyperbolic trajectories in nonautonomous flows 10:30 Thu 1 December 2016 – have the property that nearby trajectories expe- Prof Keith Burns rience exponential separation in the relevant time I will talk about the geodesic flow for the Weil- direction. Motivated by the stretching of fluid el- Petersson metric on the moduli space of a sur- ements in fluid flows, here we analyse the zone face that supports hyperbolic metrics. This is a of influence of hyperbolic trajectories. We define Riemannian metric with negative sectional curva- this to be a Hyperbolic Neighbourhood (HN), a tures. However the classical results of Anosov do time-varying region anchored to each time-varying not apply because the metric is incomplete and

4 1. Talks the sectional curvatures and their derivatives are theory of local fibre topological pressure, local en- not uniformly bounded. It was not until the 21st tropy and a variational principle (maximum local century that this geodesic flow was shown to be entropy principle). mixing (and in fact Bernoulli). I will give some ideas from the proof and also from more recent 1.9. Limit theorems for random Lasota-Yorke maps work directed towards showing that the flow is using the spectral method exponentially mixing in case of the torus with one Davor Dragiˇcević (University of New South Wales) puncture. This is joint work with Howard Masur, 15:30 Mon 28 November 2016 – Carlos Matheus, and Amie Wilkinson. Dr Davor Dragiˇcević

1.6. Specification and Markov properties in shift The so-called Nagaev-Guivarc’h spectral method spaces is one of the most powerful tools in establishing limit theorems and has been successfully applied Vaughn Climenhaga (University of Houston) in various situations including Markov chains and 11:30 Thu 1 December 2016 – dynamical systems. In the standard deterministic Asst Prof Vaughn Climenhaga setting the method consists of finding an appro- Existence, uniqueness, and statistical properties priate Banach space on which the transfer opera- of invariant measures for dynamical systems with tor has a spectral gap and then applying various hyperbolic behaviour can be studied by construct- results from the perturbation theory of linear op- ing a certain “tower” that represents the system erators. as a suspension over the full shift on a countable In this talk, I will discuss an ongoing research alphabet. I will discuss recent results that permit project which aims to extend this method to the this construction to be carried out under relatively random case. We will also explain how the multi- weak hypotheses. plicative ergodic theorem naturally appears in this setting. This is a joint work with G. Froyland, C. 1.7. Glimpse of the Infinite - the Approximation of GonzálezTokman and S. Vaienti. Invariant Sets for Delay and Partial Differential Equations 1.10. Functional Networks Michael Dellnitz (University of Paderborn) Mike Field (Imperial College London) 10:30 Tue 29 November 2016 – 16:00 Thu 1 December 2016 – Prof Michael Dellnitz Prof Mike Field In this talk we present a novel numerical frame- We describe a result that yields a functional de- work for the computation of finite dimensional composition for a large class of networks. The invariant sets for infinite dimensional dynamical result allows us to express the function of a dy- systems. With this framework we extend classical namic network in terms of dynamics of individual set oriented numerical schemes (for the computa- nodes and constituent subnetworks. tion of such objects in finite dimensions) to the Nonsmooth effects, such as changes in network infinite dimensional context. The underlying idea topology through decoupling of nodes and stop- is to utilize appropriate embedding techniques for ping and restarting of nodes, are one of the cru- the reconstruction of invariant sets in a certain fi- cial ingredients needed for this result. In net- nite dimensional space. Finally, we illustrate our works modelled by smooth dynamical systems, all approach by the computation of attractors both nodes are effectively coupled to each other at all for delay and for partial differential equations. times and information propagates instantly across the entire network. A spatiotemporal decomposi- 1.8. Random Group Actions tion is only possible if the network dynamics is Anthony Dooley (University of Technology Sydney) nonsmooth and (subsets of) nodes are allowed to 10:30 Fri 2 December 2016 – evolve independently of each other for periods of Prof Anthony Dooley time. This allows the identification of dynamical A random group action is a generalisation of units, each with its own function, that together Arnold’s theory of random dynamical systems, comprise the dynamics and function of the entire where the time dynamics is replaced by a group network. The result highlights a drawback of av- action G and the noise is non-singular under the eraging over a network: the loss of information action of G. about the individual functional units, and their temporal relations, that yield network function. In particular, with GuoHua Zhang, we showed, for the action of a discrete amenable group, that We conclude with questions about how to con- random actions have the structure of a continuous struct continuum models (smooth or stochastic bundle, realising the structure as a skew product PDEs) for functional networks that allow us to generated by the cocycle. We also developed a

5 1. Talks regain smoothness in a context where nonsmooth- 1.15. Ergodic theory in data assimilation ness is an inherent part of the network function. David Kelly (New York University) 9:00 Tue 29 November 2016 – 1.11. Some ergodic problems for stochastic PDEs Dr David Kelly Beniamin Goldys (University of Sydney) Data assimilation describes the method of blend- 10:30 Mon 28 November 2016 – ing dynamical models and observational data, Prof Beniamin Goldys with the objective of reducing uncertainty in state I will present some results on long time be- estimation and prediction. The procedure has haviour of systems evolving randomly in space and an ‘optimal’ Bayesian solution, which tends to be time described as solutions to stochastic evolution computationally intractable for high dimensional equations on. models. As a consequence, many approximation procedures, called approximate filters, have 1.12. Dynamical systems theory applied to been developed in the geoscience and numerical eigenfunction estimates weather prediction communities, where models Andrew Hassell (Australian National University) tend to be very high dimensional, and where state estimation and uncertainty quantification are cen- 14:00 Mon 28 November 2016 – tral tenets. It is important that we judge these Prof Andrew Hassell approximations on how well they inherit impor- In this talk, I will survey how results from dynam- tant features from the true Bayesian solution. In ical systems have been used to prove estimates for this talk, we will investigate ergodicity for sev- high-energy eigenfunctions on Riemannian mani- eral types of filters that are prevalent in numerical folds. weather prediction. Ergodicity is of crucial importance for filters; it implies a robustness with re- 1.13. The geometry of blenders in a spect to initial perturbations in state approxima- three-dimensional Hénon-like family tions, moreover it suggests that the filter, which Stefanie Hittmeyer (The University of Auckland) is a proxy for the true underlying dynamical sys- 15:30 Tue 29 November 2016 – tem, is inheriting important physical statistical Dr Stefanie Hittmeyer properties. Alongside mostly positive results, we will see that approximate filters don’t always do Blenders are a geometric tool to construct com- a good job of inheriting ergodicity. We define a plicated dynamics in a theoretical setting. We class of models, which are highly stable (and cer- consider an explicit family of three-dimensional tainly ergodic) for which well trusted approximate Hénon-like maps that exhibit blenders in a spe- filters exhibit strong sensitivity to initialization. cific regime in parameter space. Using advanced In other words, the filters quickly lose touch with numerical techniques we compute stable and un- reality. This talk is based on several joint works stable manifolds in this system and present one with Andy Majda, Andrew Stuart, Xin Tong, Eric of the first numerical pictures of the geometry of Vanden-Eijnden and Jonathan Weare. blenders. 1.16. Spatio-temporal computational methods for 1.14. Matching for generalised coherent sets beta-transformations PéterKoltai (Freie UniversitätBerlin) Charlene Kalle (University of Leiden) 12:00 Mon 28 November 2016 – 12:00 Tue 29 November 2016 – Dr PéterKoltai Dr Charlene Kalle The decomposition of the state space of a dy- The phenomenon of matching (i.e., merging of namical system into metastable sets is impor- left/right limits at a discontinuity after some it- tant for understanding its essential macroscopic erates) has been observed in many families with, behavior. The concept is quite well understood in some sense, nice algebraic properties. It turn for autonomous dynamical systems, and recently out that also in the family x βx + a mod 1, generalizations appeared for non-autonomous sys- matching occurs for many values7→ of β. In this tems: coherent sets. Aiming at a unified the- talk I would like to describe the mechanisms be- ory, in this talk we first present connections hind this. This is based on joint work with Henk between the measure-theoretic autonomous and Bruin and Carlo Carminati. non-autonomous concepts. We will do this by considering the augmented state space, and our results will be restricted to systems with time- periodic forcing. Second, we introduce a data- based method to compute coherent sets. It uses diffusion maps for spatio-temporal trajectory

6 1. Talks data, and it is consistent in the infinite-data limit 1.20. Lagrange and Markov dynamical spectra of with the widely-used transfer operator approach Lorenz-like attractors for coherent sets. Maria JoséPacifico (Universidade Federal do Rio de Janeiro) 1.17. Local Limit Theorem in negative curvature 14:00 Tue 29 November 2016 – Fran¸coisLedrappier (UniversitéParis 6) Dr Maria JoséPacifico 9:00 Mon 28 November 2016 – In a joint work with S. Romañoand C. G. Moreira, Prof Fran¸coisLedrappier we prove that the Hausdorff dimension of a geo- We consider the universal cover of a compact man- metric Lorenz attractor is strictaly greater than ifold with negative curvature. We give a precise 2. From this, we conclude that the interior of the equivalent of the heat kernel p(t, x, y) as t goes to Lagrange dynamical spectra as well the interior infinity. This is a joint work with Seonhee Lim of the Markov dynamical spectra of a geometric (Seoul Nat. Univ.). Lorenz attractor is non empty.

1.18. Hyperbolic billiards 1.21. Quantitative recurrence for slowly mixing Carlangelo Liverani (U. Roma “Tor Vergata”) hyperbolic systems 9:00 Wed 30 November 2016 – Fran¸coisePène (Universitéde Bretagne Prof Carlangelo Liverani Occidentale) The rigorous study of hyperbolic billiards was 9:00 Thu 1 December 2016 – started by Sinai in 1970 and since then it has Prof Fran¸coisePène grown in many directions due to the importance of We are interested in the counting process of visits this seemingly simple model for many branches of to a small around the origin, and more precisely mathematics and physics. Today it is still a very in its behaviour as the radius of the ball goes to 0. active field of research. In fact, in the last years We prove the convergence in distribution of this several new results have been obtained and new process (under a suitable time normalization) to applications have been proposed. I will present an the standard Poisson process. This is a joint work idiosyncratic selection of results and open prob- with BenoˆıtSaussol. lems concerning hyperbolic billiards. 1.22. Rigorous estimates for the Lanford map 1.19. Intrinsic excitability and the role of saddle Mark Pollicott (University of Warwick) slow manifolds 10:30 Wed 30 November 2016 – Hinke Osinga (University of Auckland) Prof Mark Pollicott 16:00 Mon 28 November 2016 – The Lanford map is a simple example of a map of Prof Hinke Osinga the interval given by Excitable cells, such as neurons, exhibit complex T x = 2x + 0.5x(1 x) (mod 1). oscillations in response to external input, e.g., − from other neurons in a network. We consider We use this as a test case to illustrate how cer- the effect of a brief stimulation from the rest state tain natural characteristics (e.g., variance, linear of a minimal neuronal model with multiple time response) can be rigorously estimated (with error scales. The transient dynamics arising from such estimates) using ideas from thermodynamic for- short current injections brings out the intrinsic malism. This is joint work with Oliver Jenkinson bursting capabilities of the system. We focus on and Polina Vytnova. transient bursts, that is, the transient generation of one or more spikes, and use a simple polynomial 1.23. Decay of Correlations in various Hard-Core model to illustrate our analysis. We take a geo- models metric approach to explain how spikes arise and Kavita Ramanan (Brown University) how their number changes as parameters are var- 9:00 Fri 2 December 2016 – ied. We discuss how the onset of new spikes is Prof Kavita Ramanan controlled by stable manifolds of a slow manifold Recently a strong connection has been established of saddle type. We give a precise definition of such for certain discrete models between the algorith- a stable manifold and use numerical continuation mic problem of counting on graphs and a certain of suitable two-point boundary value problems to correlation decay property. In particular, this approximate them. has been established for the so-called hard-core model that arises in statistical physics, telecom- munications and combinatorics, and describes a

7 1. Talks

n one-parameter family of probability measures, in- the trimmed Birkhoff sum Sbn := ϕ n k=bn+1 ◦ dexed by a positive activity parameter, on 0-1 con- T π(k) 1 with b tending to infinity and b = o (n). − n P n figurations on a graph. We present several results The proof is based on a large deviation result for on variants of the standard hard-core model, and transfer operators with spectral gap. show how dynamical systems techniques are use- These results can be applied to observables on ful for establishing the correlation decay property. subshifts of finite type and on piecewise expand- We especially focus on a continuous version of ing interval maps. In this talk I will concentrate the model, which is motivated by the algorithmic on the dynamical results. problem of computing the volume of a polytope. The talk is based on joint work with D. Gamarnik. This is joint work with Marc Kesseböhmer.

1.24. Decreasing entropy in the destruction of 1.26. Diffusive - Ballistic phase transition in a horseshoes via internal tangencies Randon Polymer model Isabel Rios (Universidade Federal Fluminense) Simone Vasconcelos da Silva (Universidade de Bras´ılia) 12:00 Wed 30 November 2016 – Prof Isabel Rios 16:00 Tue 29 November 2016 – Dr Simone Vasconcelos da Silva We study the variation of the topological entropy for a family of horseshes bifurcating an internal Phase transition issues are addressed for random tangency. We prove that, restricted to a set of polymers on the bidimensional lattice with self- parameters with total density at the breaking- repulsive interactions. By comparison with a long contact bifurcation, the topological entropy is a range one-dimensional ferromagnetic Ising model, non-increasing function. This result formalizes it is shown that in the absence of drift and with the idea that the loss of transversal homoclinic in- power law interactions, the polymer exhibits tran- tersections implies the decreasing of the amount sition from diffusive to a ballistic behavior. When of dynamics. This is a joint work with A. de Car- non-null drifts are added and positive translation valho, L. J. D´ıazand K. D´ıaz-Ordaz. invariant interactions are considered, the polymer presents a ballistic behavior. We also derive a 1.25. Generalized strong law for intermediately Central Limit Theorem for the model. trimmed Birkhoff sums 1.27. Equilibrium states on noncommutative Tanja Schindler (Australian National University) solenoids 15:30 Thu 1 December 2016 – Aidan Sims (University of Wollongong) Tanja Schindler 11:30 Fri 2 December 2016 – By a theorem by Aaronson there is no strong law Prof Aidan Sims of large numbers for observables of a dynamical system with infinite expectation. However, for KMS equilibrium states for C∗-algebraic dynami- a suitable distribution function, the sum is es- cal systems were originally motivated by physics, sentially dominated by the contribution of a fi- but have recently re-emerged as interesting in- nite number of its largest terms and a solution variants from a purely mathematical standpoint. can be obtained from a generalised strong law For example, the KMS structure of the Toeplitz of large numbers for the lightly trimmed sum, algebras of irreducible directed graphs is closely n k 1 tied up with Perron-Frobenius theory for the ad- that is, the Birkhoff sum k=1 ϕ T − trimmed by a finite number of extremes.◦ More formally, jacency matrices of the graphs, and encodes data P like the Perron-Frobenius eigenvector, the spectral we consider a permutation π n such that π(1) 1 π(n) 1 ∈ S radius and the period of the matrix. ϕ T − ... ϕ T − and consider the ◦ r ≥n ≥ ◦ π(n) 1 I’ll discuss joint work with Nathan Brownlowe sum Sn := k=r+1 ϕ T − . We say that the system fulfils a lightly◦ trimmed strong law, if there and Mitch Hawkins on the KMS structure of the P exist a real-valued sequence (dn) and r N such Toeplitz algebras of “noncommutative solenoids”. r ∈ These are are direct limits of irrational-rotation that limn Sn/dn = 1 almost surely. →∞ There is a vast literature covering the case of algebras introduced by Packer and Latrémolière, lightly trimmed strong law for independent as well and are not accessible via standard techniques as for mixing processes, one example in this area for KMS theory because of the interplay between is the lightly trimmed strong law for the digits of the subinvariance relations for the approximating the continued fractions transformation. irrational-rotation algebras, and the consistency conditions imposed by the way these subalgebras A generalisation, applicable for general distribu- nest. But a bit of work revealed a pretty picture: tion functions of a non-negative observable, is the KMS-simplex of a Toeplitz noncommutative to use intermediate trimming, that is, consider solenoid is isomorphic to the simplex of Borel

8 1. Talks probability measures on the classical solenoid. I’ll try to indicate why.

1.28. Beyond the limit of infinite time-scale separation: Edgeworth approximations and homogenisation Jeroen Wouters (University of Sydney) 11:30 Tue 29 November 2016 – Dr Jeroen Wouters Homogenization has been widely used in stochastic model reduction of slow-fast systems, including geophysical and climate systems. The theory relies on an infinite time scale separation. In this talk we present results for the realistic case of finite time scale separation. In particular, we employ Edgeworth expansions as finite size cor- rections to the central limit theorem and show improved performance of the reduced stochastic models in numerical simulations.

1.29. Large deviations beyond speciﬁcation Kenichiro Yamamoto (Nagaoka University of Technology) 11:30 Wed 30 November 2016 – Dr Kenichiro Yamamoto In this talk, we give a criterion to determine the large deviation rate functions for certain dynamical systems without the speciﬁcation property.

9 2. Posters

2.1. Optimizing Linear Response for Discrete Time Homogeneous Markov Chains Fadi Antown (University of New South Wales) 18:00 Mon 28 November 2016 – Mr Fadi Antown

2.2. Nonlinearly coupled oscillators. Peter Cudmore (The University of Queensland) 18:00 Mon 28 November 2016 – Mr Peter Cudmore

2.3. Non-singular group actions: the ergodic theorem and the critical dimension Kieran Jarrett (University of Bath) 18:00 Mon 28 November 2016 – Mr Kieran Jarrett

2.4. Fractal trees and the geometry of tilings Michael Mampusti (University of Wollongong) 18:00 Mon 28 November 2016 – Mr Michael Mampusti

2.5. TBA Eric Kwok (University of New South Wales) 18:00 Mon 28 November 2016 – Mr Eric Kwok

2.6. Fast and accurate approximation techniques for intermittent maps John Wormell (University of Sydney) 18:00 Mon 28 November 2016 – John Wormell

10 Index of Speakers

Altmann, Eduardo G. (1.1), 4 Alves, Jos´eF. (1.2), 4 Antown, Fadi (2.1), 10

Balasuriya, Sanjeeva (1.3), 4 Blumenthal, Alex (1.4), 4 Burns, Keith (1.5), 4

Climenhaga, Vaughn (1.6), 5 Cudmore, Peter (2.2), 10

Dellnitz, Michael (1.7), 5 Dooley, Anthony (1.8), 5 Dragiˇcevi´c,Davor (1.9), 5

Field, Mike (1.10), 5

Goldys, Beniamin (1.11), 6

Hassell, Andrew (1.12), 6 Hittmeyer, Stefanie (1.13), 6

Jarrett, Kieran (2.3), 10

Kalle, Charlene (1.14), 6 Kelly, David (1.15), 6 Koltai, P´eter(1.16), 6 Kwok, Eric (2.5), 10

Ledrappier, Fran¸cois(1.17), 7 Liverani, Carlangelo (1.18), 7

Mampusti, Michael (2.4), 10

Osinga, Hinke (1.19), 7

Pène,Fran¸coise(1.21), 7 Pacifico, Maria José(1.20), 7 Pollicott, Mark (1.22), 7

Ramanan, Kavita (1.23), 7 Rios, Isabel (1.24), 8

Schindler, Tanja (1.25), 8 Silva, Simone Vasconcelos da (1.26), 8 Sims, Aidan (1.27), 8

Wormell, John (2.6), 10 Wouters, Jeroen (1.28), 9

Yamamoto, Kenichiro (1.29), 9

11 A B C D E F G H

CLUNIES ROSS STREET

DICKSON 40G DICKSON PRECINCT 83 BURTON C 40F PARKING STATION & F 106 B D BRUCE 50T2 GARRAN B HALL 40 5 Accommodation 79 G 49 A E 40A 0 50 100 150m 5 C Bulk Store 50T1 D Child Minding Facility D CLOSE A C BRUCE CLOSE BARRY Sports Recreation Centre BURTON DALEY ROAD

A B COLLEGE SCIENCE 79A URSULA Student Accommodation The Andrew JOHN XXIII 45 Building Number Griffin Wing Chapel COLLEGE COLLEGE Student Administration Cockburn Bldg ROAD 47 38B Pedestrian/Bicycle Path 116 Union Court Retail Facilities BURGMANN 51 133 44 103 COLLEGE Free Bus Stop 50 44A 42 LANE Sullivan's PHYSICS BBQ Sites LINNAEUS WAY ROAD Creek 52 Chapel 141 PSYCHOLOGY 48A 42A 39 38 Emergency Phone Lindsay Pryor Walk 134

FORESTRY AVENUE ANU Security ROAD 136 39A 38A 35 DALEY 36

LANE 48 BOAT SHED 82 138 BIRCH Bicycle Enclosure Gardeners Soil Depot CLOSE CUNNINGHAM Visitor Parking ROAD 46E P Lake BIOLOGY HANCOCK NUCLEAR McPherson FULTON Multi Storey Parking Station 58E Bridge 34 33-2 35A 95 PHYSICS BOATHOUSE 43 57 137 115 MUIR 4 Burley PARKES 58A 46N 33A Surface Car Parking GARRAN 54E 46 33-1 RSISE 4 84 COCKROFT58F SULLIVANS 135 ROAD 46C 122 59 56A From Fenner Hall ST

Griffin 143 PLACE 58C 131B 46H 108 McCAUGHEY

56B 45A UNIVERSITY CSIT 58 B JOHN CURTIN SCHOOL 88 45 31 58B MEDICAL RESEARCH WARD 46I 58D 56 46G Bank/ATM FLOREY 131 ROAD P ENGINEERING GEOLOGY CLOSE OLIPHANT 60 P P 19B JOHN CURTIN RD 131A 32 North 88T1 ROAD Tennis Dentist South CREEK Courts Pavilion 54 Oval A NORTH

Food Outlet 87 Canberry 16T DRIVE Bridge 16 + DAVE COCKING Jaeger 6 ARTS 18 19 ANU SPORT & REC North Jaeger 1 53 19A Jaeger 7 188 CENTRE CENTRE Willows + Medical Centre RSES 125 188A P Oval Jaeger 2 ROAD ANTHONY LOW Fellows Oval 61 62 Jaeger 4 62A 124 Oval 90 02 MiniMart Jaeger 5 FELLOWS UNION SHRIMP III EGGLESTON 117 Tennis LANE JB CHIFLEY Union WAY 89 3 Courts 3L 17 Court UNION 113 Jaeger ROAD 15 20 3K LANECONCESSIONS MANNING Newsagent Jaeger 8 Walk Winston Denis 3 63T1 7 6 CLARKE 3 MILLS GARRAN 61C 142 3J LANE OHB A 6A 26A 63 Pharmacy 63T2 63A 118 McDONALD OLD 61A GRADUATE 3H 14 21 27 Tennis 3I 10C HOUSE ADMINISTRATION J DEDMAN Court ROAD 10B 10T1 26B 30 Post Office 3G 5 AVENUE 64 2 PAULINE MELVILLE 22 64A R.G LAW 10A GRIFFIN HALL TOAD

EAST HOPE A.D. 80 97 MENZIES 29 HALL ROAD 26C CHANCELRY 127 11 12 23 PLACE 13T1 DRILL HALL MAIN P 10 P ST BAL 64B GALLERY CLOSE

COOMBS ROAD PLACE CHANCELRY CRESCENT 26 KINGSLEY STREET

65 72 HAYDON-ALLEN LANE BALDESSIN UNDERGROUND BALMAIN FELLOWS PARKING STATION 13A CLOSE 13T 25 109 UNIVERSITY WARRUMBUL WATSON 66 110 99 BERYL LENA KARMEL

24 STREET NATIONAL 8 RAWSON 25A LODGE 01C HOUSE 13 STREET 01B KINGSLEY ST LODGE SECURITY 67 1 8A KINGSLEY PLACE X003 COLLEGE 105D 13B UNIVERSITY PARKING STATION X004 To Fenner Hall 9 FAMILY LAW 71 CRES 1A H.C.COOMBS 67A 101B 101A P SCH COURT KINLOCH LANE CRAWFORD 132A OF 105A STREET DAVEY 69A 130 ELLERY P SCHOOL ANZSOG 71T ART THEATRE X001 LODGE 2 37 BALMAIN 101 2 67B 93 105 X002 RIMMER 69 70 LODGE CHILDERS 132 67C 68 HUTTON UNDERGROUND 74 76 STREET CHILDERS STREET McCOY ANU Judith Wright P CHILDERS X005 73A LIVERSIDGE 1 Student OLD 5 Court 3 Administration 73 2 SQUARE 121

73C BACHELORS STREET STREET

PLACE HERBERT CANBERRA NATIONAL FILM WILLIAM A 4 P Civic Early Child 126 CRES MARCUS C B 18 & HOUSE 128 CLARKE Care Centre Liversidge Court AVENUE RUDD 78 16 SOUND ARCHIVE 105C 100 F 81 77A E D SCH 121 27 77 OF PARKES 23 25 105B MUSIC LEWIS International CROSSING 28 LANE BRIAN ALINGA Sculpture LENNOX ALLSOP LANE STREET Park HOUSE CLARKE 75A CIRC.

120SIR ROLAND ST ST

75D 75F CRESCENT WILSON BLDG GORDON MULWALA PLACE 75I MURDEN WILDEN STREET AUSTRALIAN ENS ST PLACE LEM DARWIN PLACE MOORE

WAY C LENNOX ACADEMY 1 75H UNIVERSITY 1 75E OF SCIENCE ST M 75G HALES IA L L 75T2 I FARRELL AVENUE IAN POTTER W STREET HOBART EDINBURGH AVEHOUSE LONDON CIRCUIT STREET 75T1 LAWSON

MARCUS

NORTHBOURNE Facilities & Services February 2015 KNOWLES PLACE A B C D E F G H