| Preface | |
| Hyperbolic Fixed Points of Diffeomorphisms and their Stable and Unstable Manifolds | p. 1 |
| Examples of Diffeomorphisms | p. 1 |
| Definition and Examples of Hyperbolic Fixed Points | p. 2 |
| Definition of Stable and Unstable Manifolds | p. 3 |
| The Saddle-Point Property | p. 5 |
| Smoothness of the Local Stable Manifold | p. 12 |
| Diffeomorphisms depending on a Parameter | p. 17 |
| Hyperbolic Sets of Diffeomorphisms | p. 21 |
| Definition of Hyperbolic Set | p. 21 |
| Boundedness of the Projection | p. 24 |
| Continuity of the Projection | p. 25 |
| Exponential Dichotomies for Difference Equations | p. 29 |
| Expansivity Property of Hyperbolic Sets | p. 41 |
| Roughness of Hyperbolic Sets | p. 44 |
| Transversal Homoclinic Points of Diffeomorphisms and Hyperbolic Sets | p. 57 |
| The Hyperbolic Set associated with a Transversal Homoclinic Point | p. 57 |
| The Construction of Diffeomorphisms with Transversal Homoclinic Points | p. 64 |
| An Example from Differential Equations | p. 72 |
| The Shadowing Theorem for Hyperbolic Sets of Diffeomorphisms | p. 77 |
| The Shadowing Theorem | p. 77 |
| More on the Roughness of Hyperbolic Sets | p. 83 |
| Asymptotic Phase for Hyperbolic Sets | p. 88 |
| Symbolic Dynamics Near a Transversal Homoclinic Point of a Diffeomorphism | p. 91 |
| Hyperbolic Periodic Orbits of Ordinary Differential Equations, Stable and Unstable Manifolds and Asymptotic Phase | p. 99 |
| The Poincare Map | p. 100 |
| Hyperbolic Periodic Orbits and Their Stable and Unstable Manifolds | p. 104 |
| Asymptotic Phase and the Stable and Unstable Foliations | p. 109 |
| Hyperbolic Sets of Ordinary Differential Equations | p. 115 |
| Definition of Hyperbolic Set | p. 115 |
| Boundedness of the Projections | p. 118 |
| Continuity of the Projections | p. 121 |
| Exponential Dichotomies for Differential Equations | p. 126 |
| Expansivity Property of Hyperbolic Sets | p. 149 |
| Roughness of Hyperbolic Sets | p. 160 |
| Transversal Homoclinic Points and Hyperbolic Sets in Differential Equations | p. 171 |
| The Hyperbolic Set associated with a Transversal Homoclinic Orbit | p. 171 |
| The Construction of a Differential Equation with a Transversal Homoclinic Orbit | p. 181 |
| Shadowing Theorems for Hyperbolic Sets of Differential Equations | p. 187 |
| The Discrete Shadowing Theorem | p. 187 |
| The Continuous Shadowing Theorem | p. 198 |
| More on the Roughness of Hyperbolic Sets | p. 206 |
| Asymptotic Phase for Hyperbolic Sets | p. 218 |
| Symbolic Dynamics Near a Transversal Homoclinic Orbit of a System of Ordinary Differential Equations | p. 225 |
| Numerical Shadowing | p. 241 |
| Finite Time Shadowing for Maps | p. 241 |
| Periodic Shadowing for Maps | p. 248 |
| Finite Time Shadowing for Differential Equations | p. 255 |
| Periodic Shadowing for Differential Equations | p. 263 |
| Rigorous Verification of Chaotic Behaviour | p. 270 |
| References | p. 285 |
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