Preface -- Nomenclature -- 1 Dynamical systems -- 1.1 Main definitions -- 1.2 Embedding of a discrete dynamical system into a flow -- 1.3 Local Poincaré diffeomorphism -- 1.4 Time-periodic systems of differential equations -- 1.5 Action of an Abelian group -- 2 Topologies on spaces of dynamical systems -- 2.1 C0-topology -- 2.2 C1-topology -- 2.3 Metrics on the space of systems of differential equations -- 2.4 Generic properties -- 2.5 Immersions and embeddings -- 3 Equivalence relations -- 3.1 Topological conjugacy -- 3.2 Topological equivalence of flows -- 3.3 Nonwandering set -- 3.4 Local equivalence -- 4 Hyperbolic fixed point -- 4.1 Hyperbolic linear mapping -- 4.2 The Grobman-Hartman theorem -- 4.3 Neighborhood of a hyperbolic fixed point -- 4.4 The stable manifold theorem -- 4.5 Hyperbolic periodic point -- 5 Hyperbolic rest point and hyperbolic closed trajectory -- 5.1 Hyperbolic rest point -- 5.2 Hyperbolic closed trajectory -- 6 Transversality -- 6.1 Transversality of mappings and submanifolds -- 6.2 Transversality condition -- 6.3 Palis lemma -- 6.4 Transversality and hyperbolicity for one-dimensional mappings -- 7 Hyperbolic sets -- 7.1 Definition of a hyperbolic set -- 7.2 Examples of hyperbolic sets -- 7.3 Basic properties of hyperbolic sets -- 7.4 Stable manifold theorem -- 7.5 Axiom A -- 7.6 Hyperbolic sets of flows -- 8 Anosov diffeomorphisms -- 9 Smale's horseshoe and chaos -- 9.1 Smale's horseshoe -- 9.2 Chaotic sets -- 9.3 Homoclinic points -- 10 Closing Lemma -- 11 C0-generic properties of dynamical systems -- 11.1 Hausdorff metric -- 11.2 Semicontinuous mappings -- 11.3 Tolerance stability and Takens' theory -- 11.4 Attractors of dynamical systems -- 12 Shadowing of pseudotrajectories in dynamical systems -- 12.1 Definitions and results -- 12.2 Proof of Theorem 12.1.

12.3 Proof of Theorem 12.2 -- 12.4 Proof of Theorem 12.3 -- A Scheme of the proof of the Mane theorem -- B Lectures on the history of differential equations and dynamical systems -- B.1 Differential equations and Newton's anagram -- B.2 Development of the general theory -- B.3 Linear equations and systems -- B.4 Stability -- B.5 Nonlocal qualitative theory. Dynamical systems -- B.6 Structural stability -- B.7 Dynamical systems with chaotic behavior -- Bibliography -- Index.