ABCD springer.com LONDON BOOKFAIR 2011 Title Selection - MATHEMATICS Springer Rights and Permissions | Springer-Verlag GmbH | Tiergartenstr. 17 | 69121 Heidelberg | GERMANY | [email protected] springer.com 2 A.A. Agrachev, Y. Sachkov subsets" of the phase space. Such systems lead to com- V. Arnol'd, S. Novikov plicated motion (so-called "chaos"). The book begins Control Theory from the with a discussion of the topological manifestations Dynamical Systems VII Geometric Viewpoint of uniform and total hyperbolicity: hyperbolic sets, Integrable Systems. Nonholonomic Dynamical Smale's Axiom A, structurally stable systems, Anosov Systems This book presents some facts and methods of Math- systems, and hyperbolic attractors of dimension or ematical Control Theory treated from the geomet- codimension one. There are various modifications of This volume contains five surveys on dynamical sys- ric viewpoint. It is devoted to finite-dimensional hyperbolicity and in this connection the properties tems. The first one deals with nonholonomic mechan- deterministic control systems governed by smooth of Lorenz attractors, pseudo-analytic Thurston dif- ics and gives an updated and systematic treatment ordinary differential equations. The problems of con- feomorphisms, and homogeneous flows with expand- ofthe geometry of distributions and of variational trollability, state and feedback equivalence, and opti- ing and contracting foliations are investigated. These problems with nonintegrable constraints. The mod- mal control are studied. Some of the topics treated by last two questions are discussed in the general context ern language of differential geometry used throughout the authors are covered in monographic or textbook of the theory of homeomorphisms of surfaces and of the survey allows for a clear and unified exposition of literature for the first time while others are presented homogeneous flows. the earlier work on nonholonomic problems. There is a detailed discussion of the dynamical properties in a more general and flexible setting than elsewhere. More on www.springer.com/978-3-642-08168-2 Although being fundamentally written for mathe- of the nonholonomic geodesic flow and of various maticians, the authors make an attempt to reach both Available related concepts, such as nonholonomic exponen- the practitioner and the theoretician by blending the 1995. VII, 235 p. 39 illus. (Encyclopaedia of Mathematical tial mapping, nonholonomic sphere, etc. Other sur- theory with applications. They maintain a good bal- Sciences, 66) veys treat various aspects of integrable Hamiltonian ance between the mathematical integrity of the text 978-3-642-08168-2 ▶ 109,95 € systems, with an emphasis on Lie-algebraic construc- and the conceptual simplicity that might be required tions. Among the topics covered are: the generalized by engineers. It can be used as a text for graduate Calogero-Moser systems based on root systems of courses and will become most valuable as a reference simple Lie algebras, a ge- neral r-matrix scheme for work for graduate students and researchers. constructing integrable systems and Lax pairs, links with finite-gap integration theory, topologicalaspects More on www.springer.com/978-3-642-05907-0 of integrable systems, integrable tops, etc. One of Available the surveys gives a thorough analysis of a family of 2004. XIV, 412 p. 35 illus. (Encyclopaedia of Mathematical quantum integrable systems (Toda lattices) using the Sciences, 87) machinery of representation theory. Readers will find 978-3-642-05907-0 ▶ 119,95 € all the new differential geometric and Lie-algebraic methods which are currently used in the theory of integrable systems in this book. It will be indispens- able to graduate students and researchers in mathe- matics and theoretical physics. E. Arbarello, M. Cornalba, P.A. Griffiths More on www.springer.com/978-3-642-05738-0 Available T.S. Angell, A. Kirsch Geometry of Algebraic Curves 1994. VII, 341 p. 9 illus. (Encyclopaedia of Mathematical Volume II with a contribution by Joseph Daniel Sciences, 16) Optimization Methods in Harris 978-3-642-05738-0 ▶ 104,95 € Electromagnetic Radiation The second volume of the Geometry of Algebraic Curves is devoted to the foundations of the theory of This book considers problems of optimization aris- moduli of algebraic curves. Its authors are research ing in the design of electromagnetic radiators and mathematicians who have actively participated in the receivers. The authors develop a systematic general development of the Geometry of Algebraic Curves. theory that can be applied to a wide class of struc- The subject is an extremely fertile and active one, both tures. The theory is illustrated with familiar, simple within the mathematical community and at the inter- W. Arveson examples and indications of how the results can be face with the theoretical physics community. The applied to more complicated structures. The final approach is unique in its blending of algebro-geo- Noncommutative Dynamics and chapter introduces techniques from multicriteria opti- metric, complex analytic and topological/combi- mization in antenna design. The material is intended natorial methods. It treats important topics such as E-Semigroups for a dual audience of mathematicians and theoreti- Teichmüller theory, the cellular decomposition of The term Noncommutative Dynamics can be inter- cally-inclined engineers. References to both the math- moduli and its consequences and the Witten conjec- ematics and engineering literature help guide the preted in several ways. It is used in this book to refer ture. The careful and comprehensive presentation of to a set of phenomena associated with the dynamics reader through the necessary mathematical back- the material will be of value to students who wish to ground. of quantum systems of the simplest kind that involve learn the subject and to experts as a reference source. rigorous mathematical structures associated with More on www.springer.com/978-1-4419-1914-4 The first volume appeared 1985 as volume 267 of the infinitely many degrees of freedom. The dynamics Due April 2011 same series. of such a system is represented by a one-parameter 2004. 331 p. 92 illus. (Springer Monographs in More on www.springer.com/978-3-540-42688-2 group of automorphisms of a noncommutative alge- Mathematics, ) Due April 2011 bra of observables, and the author focuses primarily 978-1-4419-1914-4 ▶ 84,95 € on the most concrete case in which that algebra con- 2011. XXX, 963 p. (Grundlehren der mathematischen sists of all bounded operators on a Hilbert space. This Wissenschaften, 268) subject overlaps with several mathematical areas of 978-3-540-42688-2 ▶ 89,95 € current interest, including quantum field theory, the D. Anosov dynamics of open quantum systems, noncommuta- tive geometry, and both classical and noncommuta- Dynamical Systems IX tive probability theory. This is the first book to give Dynamical Systems with Hyperbolic Behaviour a systematic presentation of progress during the past The book deals with smooth dynamical systems with fifteen years on the classification of E-semigroups up hyperbolic behaviour of trajectories filling out "large to cocycle conjugacy. There are many new results that springer.com 3 cannot be found in the existing literature, as well as ing a detailed exposition of many of the cohomolog- significant reformulations and simplifications of the ical results one obtains from having a torus action theory as it exists today. William Arveson is Profes- with fixed points. Many examples, such as toric vari- sor of Mathematics at the University of California, eties and flag varieties, are discussed in detail. W.M. Berkeley. He has published two previous books with McGovern studies the actions of a semisimple Lie Springer-Verlag, An Invitation to C*-algebras (1976) or algebraic group on its Lie algebra via the adjoint and A Short Course on Spectral Theory (2001). action and on itself via conjugation. His contribution More on www.springer.com/978-1-4419-1803-1 focuses primarily on nilpotent orbits that have found the widest application to representation theory in the Due April 2011 last thirty-five years. 2003. X, 434 p. (Springer Monographs in Mathematics, ) More on www.springer.com/978-3-642-07745-6 978-1-4419-1803-1 ▶ 91,95 € M. Bartholomew-Biggs Available Nonlinear Optimization with 2002. V, 242 p. (Encyclopaedia of Mathematical Sciences, 131) Engineering Applications 978-3-642-07745-6 ▶ 104,95 € This textbook examines a broad range of problems in science and engineering, describing key numer- ical methods applied to real life. The case studies presented are in such areas as data fitting, vehicle route planning and optimal control, scheduling and resource allocation, sensitivity calculations and worst-case analysis.Among the main topics covered:* one-variable optimization — optimality conditions, direct search and gradient * unconstrained optimiza- tion in n variables — solution methods including H. Bahouri, J. Chemin, R. Danchin Nelder and Mead simplex, steepest descent, New- ton, Gauss–Newton, and quasi-Newton techniques, Fourier Analysis and Nonlinear trust regions and conjugate gradients * constrained Partial Differential Equations optimization in n variables — solution methods including reduced-gradients, penalty and barrier T.R. Bielecki, M. Rutkowski In recent years, the Fourier analysis methods have methods, sequential quadratic programming, and expereinced a growing interest in the study of par- interior point techniques * an introduction