| Preface | p. VII |
| Introduction | p. 1 |
| Exponential contractions | p. 2 |
| Exponential dichotomies and stable manifolds | p. 4 |
| Topological conjugacies | p. 7 |
| Center manifolds, symmetry and reversibility | p. 10 |
| Lyapunov regularity and stability theory | p. 13 |
| Exponential dichotomies | |
| Exponential dichotomies and basic properties | p. 19 |
| Nonuniform exponential dichotomies | p. 19 |
| Stable and unstable subspaces | p. 22 |
| Existence of dichotomies and ergodic theory | p. 24 |
| Robustness of nonuniform exponential dichotomies | p. 27 |
| Robustness in semi-infinite intervals | p. 27 |
| Formulation of the results | p. 27 |
| Proofs | p. 29 |
| Stable and unstable subspaces | p. 40 |
| Robustness in the line | p. 42 |
| The case of strong dichotomies | p. 49 |
| Stable manifolds and topological conjugacies | |
| Lipschitz stable manifolds | p. 55 |
| Setup and standing assumptions | p. 55 |
| Existence of Lipschitz stable manifolds | p. 56 |
| Nonuniformly hyperbolic trajectories | p. 59 |
| Proof of the existence of stable manifolds | p. 61 |
| Preliminaries | p. 61 |
| Solution on the stable direction | p. 62 |
| Behavior under perturbations of the data | p. 64 |
| Reduction to an equivalent problem | p. 67 |
| Construction of the stable manifolds | p. 69 |
| Existence of Lipschitz unstable manifolds | p. 71 |
| Smooth stable manifolds in R[superscript n] | p. 75 |
| C[superscript 1] stable manifolds | p. 75 |
| Nonuniformly hyperbolic trajectories | p. 77 |
| Example of a C[superscript 1] flow with stable manifolds | p. 78 |
| Proof of the C[superscript 1] regularity | p. 79 |
| A priori control of derivatives and auxiliary estimates | p. 79 |
| Lyapunov norms | p. 83 |
| Existence of an invariant family of cones | p. 86 |
| Construction and continuity of the stable spaces | p. 92 |
| Behavior of the tangent sets | p. 95 |
| C[superscript 1] regularity of the stable manifolds | p. 100 |
| C[superscript k] stable manifolds | p. 102 |
| Proof of the C[superscript k] regularity | p. 106 |
| Method of proof | p. 106 |
| Linear extension of the vector field | p. 107 |
| Characterization of the stable spaces | p. 110 |
| Tangential component of the extension | p. 111 |
| C[superscript k] regularity of the stable manifolds | p. 116 |
| Smooth stable manifolds in Banach spaces | p. 119 |
| Existence of smooth stable manifolds | p. 120 |
| Nonuniformly hyperbolic trajectories | p. 121 |
| Proof of the existence of smooth stable manifolds | p. 123 |
| Functional spaces | p. 123 |
| Derivatives of compositions | p. 125 |
| A priori control of the derivatives | p. 127 |
| Holder regularity of the top derivatives | p. 129 |
| Solution on the stable direction | p. 133 |
| Behavior under perturbations of the data | p. 136 |
| Construction of the stable manifolds | p. 138 |
| A nonautonomous Grobman-Hartman theorem | p. 145 |
| Conjugacies for flows | p. 145 |
| Conjugacies for maps | p. 146 |
| Setup | p. 147 |
| Existence of topological conjugacies | p. 149 |
| Holder regularity of the conjugacies | p. 155 |
| Main statement | p. 155 |
| Lyapunov norms | p. 156 |
| Proof of the Holder regularity | p. 157 |
| Proofs of the results for flows | p. 162 |
| Reduction to discrete time | p. 162 |
| Proofs | p. 164 |
| Center manifolds, symmetry and reversibility | |
| Center manifolds in Banach spaces | p. 171 |
| Standing assumptions | p. 171 |
| Existence of center manifolds | p. 173 |
| Proof of the existence of center manifolds | p. 176 |
| Functional spaces | p. 176 |
| Lipschitz property of the derivatives | p. 179 |
| Solution on the central direction | p. 184 |
| Reduction to an equivalent problem | p. 187 |
| Construction of the center manifolds | p. 191 |
| Reversibility and equivariance in center manifolds | p. 197 |
| Reversibility for nonautonomous equations | p. 197 |
| The notion of reversibility | p. 197 |
| Relation with the autonomous case | p. 199 |
| Nonautonomous reversible equations | p. 201 |
| Reversibility in center manifolds | p. 202 |
| Formulation of the main result | p. 202 |
| Auxiliary results | p. 206 |
| Proof of the reversibility | p. 212 |
| Equivariance for nonautonomous equations | p. 213 |
| Equivariance in center manifolds | p. 214 |
| Lyapunov regularity and stability theory | |
| Lyapunov regularity and exponential dichotomies | p. 219 |
| Lyapunov exponents and regularity | p. 219 |
| Existence of nonuniform exponential dichotomies | p. 222 |
| Bounds for the regularity coefficient | p. 226 |
| Lower bound | p. 226 |
| Upper bound in the triangular case | p. 227 |
| Reduction to the triangular case | p. 232 |
| Characterizations of regularity | p. 235 |
| Equations with negative Lyapunov exponents | p. 241 |
| Lipschitz stable manifolds | p. 242 |
| Smooth stable manifolds | p. 243 |
| Measure-preserving flows | p. 244 |
| Lyapunov regularity in Hilbert spaces | p. 249 |
| The notion of regularity | p. 249 |
| Upper triangular reduction | p. 252 |
| Regularity coefficient and Perron coefficient | p. 254 |
| Characterizations of regularity | p. 256 |
| Lower and upper bounds for the coefficients | p. 259 |
| Stability of nonautonomous equations in Hilbert spaces | p. 265 |
| Setup | p. 265 |
| Stability results | p. 267 |
| Smallness of the perturbation | p. 268 |
| Norm estimates for the evolution operators | p. 270 |
| Proofs of the stability results | p. 273 |
| References | p. 277 |
| Index | p. 283 |
| Table of Contents provided by Ingram. All Rights Reserved. |
