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| Introduction | |
| Topological properties of flows and cascades in the vicinity of a rest point and a periodic trajectory | |
| Basic definitions and facts | p. 1 |
| Hyperbolic rest points | p. 8 |
| Floquet-Lyapunov theory | p. 13 |
| Hadamard-Bohl-Perron theory | p. 21 |
| Finitely smooth normal forms of vector fields and diffeomorphisms | |
| The problem on reducing a C[superscript[infinity]] vector field to C[superscript k] normal form in the vicinity of a hyperbolic rest point | p. 29 |
| Normalization of jets of vector fields and diffeomorphisms | p. 34 |
| Polynomial normal forms | p. 47 |
| Simplification of the resonant normal form via finitely smooth transformations | p. 67 |
| A general condition for C[superscript k] linearizability | p. 76 |
| C[superscript k] linearization theorems | p. 89 |
| Some sufficient conditions for C[superscript k] linearizability | p. 108 |
| Theorems on C[superscript k] normal forms | p. 136 |
| Linearization of finitely smooth vector fields and diffeomorphisms | p. 143 |
| Normal forms (a supplement to [section] 8) | p. 178 |
| Summary of results on finitely smooth normal forms | p. 182 |
| Linear extensions of dynamical systems | |
| Basic notions and facts | p. 193 |
| Exponential separation and exponential splitting | p. 200 |
| The structure of linear extensions | p. 206 |
| Quadratic Lyapunov functions | p. 224 |
| Weak regularity and Green-Samoilenko functions | p. 230 |
| Smooth linear extensions | p. 251 |
| Invariant subbundles of weakly non-linear extensions | |
| Invariant subbundles and their intrinsic characterization | p. 261 |
| The decomposition theorem | p. 268 |
| The Grobman-Hartman theorem | p. 274 |
| Smooth invariant subbundles | p. 278 |
| Invariant manifolds | |
| Persistence of invariant manifolds | p. 290 |
| Normal hyperbolicity and persistence | p. 293 |
| Necessary condition for persistence | p. 300 |
| Asymptotic phase | p. 304 |
| Normal forms in the vicinity of an invariant manifold | |
| Polynomial normal forms (the nodal case) | p. 318 |
| Polynomial normal forms (the saddle case) | p. 332 |
| Appendix. Some facts from global analysis | p. 343 |
| Bibliography | p. 364 |
| Subject index | p. 380 |
| List of symbols | p. 384 |
| Table of Contents provided by Blackwell. All Rights Reserved. |
