Smooth Dynamical SystemsThis is a reprint of M C Irwin's beautiful book, first published in 1980. The material covered continues to provide the basis for current research in the mathematics of dynamical systems. The book is essential reading for all who want to master this area. |
Contents
| 1 | |
Chapter 1 Some Simple Examples | 12 |
Chapter 2 Equivalent Systems | 28 |
Chapter 3 Integration of Vector Fields | 57 |
Chapter 4 Linear Systems | 80 |
Chapter 5 Linearization | 109 |
Chapter 6 Stable Manifolds | 143 |
Chapter 7 Stable Systems | 161 |
Appendix A Theory of Manifolds | 196 |
Appendix B Map Spaces | 225 |
Appendix C The Contraction Mapping Theorem | 239 |
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Common terms and phrases
admissible chart Appendix automorphism Banach space basic set bifurcation Chapter closed orbit continuous linear continuous map Corollary deduce defined definition denote dense diffeomorphism differential equations dynamical systems embedding equivalence classes equivalence relation example Exercise fibre Figure finite dimensional flow equivalence function given GL(E global Hausdorff hence HL(E homeomorphism hyperbolic fixed point hyperbolic linear induced integral curve integral flow intersection isomorphism Lemma Let f Liapunov linear automorphism Lipschitz with constant map f map g Math metric Morse–Smale non-empty norm open neighbourhood open subset or(T periodic points perturbation phase portrait phism Proof Proposition Prove respect restriction Riemannian sequence Smale smooth stable manifold theorem stable set stable summand structurally stable submanifold subspace Suppose tangent bundle theory Tºf topological conjugacy topological equivalence topological space topologically conjugate trivial unique unstable vector bundle vector field velocity zero