Geometric theory of dynamical systems
Software (see DSWeb):
AUTO and related (XPPAut, DSTool, PyDSTool)
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
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