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Geometric theory of dynamical systems

A brief history.

Software (see DSWeb):

AUTO and related (XPPAut, DSTool, PyDSTool)

CONTENT

Introductory

Jost, Dynamical Systems: Examples of Complex Behaviour

Broer and Takens, Dynamical systems and chaos

Hartman, Ordinary differential equations

Lefschetz, Differential equations: geometric theory

Arnold, Geometrical methods in the theory of differential equations

Teschl, Ordinary Differential Equations and Dynamical Systems

Hirsch and Smale, Differential Equations, Dynamical Systems, and Linear Algebra

Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos

Hale & Kocac, Dynamics and bifurcations

Barreira & Valls, Dynamical systems: an introduction

Ruelle, Chaotic evolution and strange attractors

Intermediate to advanced

General

Guckenheimer and Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields

Palis & de Melo, Geometric theory of dynamical systems: an introduction

Katok and Hasselblatt, Introduction to the Modern Theory of Dynamical Systems

Brin and Stuck, Introduction to dynamical systems

Robinson, Dynamical systems

Nitecki, Differential dynamics

Shub, Global stability of dynamical systems

De Vries, Topological dynamical systems

Akin, The general topology of dynamical systems

Bifurcation theory

Golubitski and Guillemin, Stable mappings and their singularities

Ruelle, Elements of differentiable dynamics and bifurcation theory

Wiggins, Global bifurcations and chaos

Kuznetzov, Elements of applied bifurcation theory

Chow and Hale, Methods of bifurcation theory

Murdock, Normal forms and unfoldings for local dynamical systems

Applied and computational

Perko, Differential Equations and Dynamical Systems

Alligood, Sauer and Yorke: Chaos: an introduction to dynamical systems

Meiss, Differential dynamical systems

Ergodic theory

Walters, An introduction to ergodic theory

Petersen, Ergodic theory

Mane, Ergodic theory and differentiable dynamics

Barreira and Pesin, Introduction to smooth ergodic theory

Ding and Zhou, Statistical properties of deterministic systems

Einsiedler and Ward, Ergodic theory: with a view towards number theory

Viana and Oliveira, Foundations of ergodic theory

Pollicott and Yuri, Dynamical systems and ergodic theory

Cornfield, Fomin, Sinai, Ergodic theory

Sinai, Topics in ergodic theory

Bowen, Chazottes and Ruelle, Equilibrium states and the ergodic theory of Anosov diffeomorphisms

Hasselblatt (ed), Ergodic Theory and Negative Curvature

Aaronson, An introduction to infinite ergodic theory

Advanced and special topics

De Melo and Strien, One-dimensional dynamics

Abraham and Robin, Transversal mappings and flows

Palis and Takens, Hyperbolicity and Sensitive Chaotic Dynamics at Homoclinic Bifurcations

Pesin, Lectures on partial hyperbolicity and stable ergodicity

Bonatti, Diaz, Viana, Dynamics Beyond Uniform Hyperbolicity

Abstract theory of global attractors

Neerven, The asymptotic behavior of semigroups of linear operators

Robinson, Infinite-dimensional dynamical systems

Sell and You, Dynamics of evolutionary equations

Babin and Vishik (eds), Attractors of evolution equations

Ladyzhenskaya, Attractors for semigroups and evolution equations

Hale, Asymptotic behavior of dissipative systems

Temam, Infinite-dimensional dynamical systems in mechanics and physics

Raugel, Global attractors in partial differential equations

Symbolic dynamics

Bedford et al (eds), Ergodic Theory, Symbolic Dynamics, and Hyperbolic Spaces

Coornaert and Papadopoulos, Symbolic Dynamics and Hyperbolic Groups

The Russian series

Anosov and Arnold (eds), Dynamical Systems I: Ordinary Differential Equations and Smooth Dynamical Systems

Sinai (ed), Dynamical systems II: Ergodic Theory with Applications to Dynamical Systems and Statistical Mechanics

Arnold(ed), Dynamical Systems III: Mathematical Aspects of Classical and Celestial Mechanics

Arnold and Novikov (eds), Dynamical Systems IV: Symplectic Geometry & Its Applications

Arnold (ed), Dynamical systems V: Bifurcation Theory and Catastrophe Theory

Arnold (ed), Dynamical Systems VI: Singularity Theory I

Arnold and Novikov (eds), Dynamical Systems VII: Integrable Systems Nonholonomic Dynamical Systems

Arnold (ed), Dynamical Systems VIII: Singularity Theory II. Applications

Anosov (ed), Dynamical systems IX: Dynamical Systems with Hyperbolic Behaviour

Kozlov (ed), Dynamical Systems X: General Theory of Vortices

Encyclopedic

The Handbook of dynamical systems

Some classical papers

Smale, Differentiable dynamical systems

Ruelle, Small random perturbations of dynamical systems and the definition of attractor

Milnor, On the concept of attractor

Milnor, On the concept of attractor: Correction and remarks

Hurley, Attractors: persistence and density of their basins

Conley, Isolated invariant sets and the Morse index