Prepared for submission to JHEP Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow Alireza Behtash1;2 C. N. Cruz-Camacho3 M. Martinez1 1 Department of Physics, North Carolina State University, Raleigh, NC 27695, USA 2Kavli Institute for Theoretical Physics University of California, Santa Barbara, CA 93106, USA 3Universidad Nacional de Colombia, Sede Bogot´a,Facultad de Ciencias, Departamento de F´ısica, Grupo de F´ısica Nuclear, Carrera 45 N o 26-85, Edificio Uriel Guti´errez, Bogot´a D.C. C.P. 1101, Colombia E-mail:
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[email protected] Abstract: The non-equilibrium attractors of systems undergoing Gubser flow within relativistic kinetic theory are studied. In doing so we employ well-established methods of nonlinear dynamical systems which rely on finding the fixed points, investigating the structure of the flow diagrams of the evolution equations, and characterizing the basin of attraction using a Lyapunov function near the stable fixed points. We obtain the attractors of anisotropic hydrodynamics, Israel-Stewart (IS) and transient fluid (DNMR) theories and show that they are indeed non-planar and the basin of attraction is essentially three dimensional. The attractors of each hydrodynamical model are compared with the one obtained from the exact Gubser solution of the Boltzmann equation within the relaxation time approximation. We observe that the anisotropic hydrodynamics is able to match up to high numerical accuracy the attractor of the exact solution while the second order hydrodynamical theories fail to describe it. We show that the IS and DNMR asymptotic series expansion diverge and use resurgence techniques to perform the resummation of these divergences.