## Smooth dynamical systemsSmooth dynamical systems |

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### Contents

1 | |

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 |

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253 | |

### Common terms and phrases

admissible chart Appendix automorphism Banach space basic set bifurcation C"-bounded called Chapter closed orbit continuous linear continuous map Corollary deduce defined definition denote dense diffeomorphism differential dynamical system eigenvalues embedding equations equivalence classes equivalence relation example Exercise fibre Figure finite dimensional flow equivalence function given GL(E GL(R Hausdorff hence HL(E homeomorphism hyperbolic fixed point induced integral curve integral flow intersection isomorphism Lemma Let f Liapunov Lipschitz with constant map f map g mapping theorem Morse–Smale non-empty non-wandering set norm open neighbourhood open subset or(T orientation preserving periodic points perturbation phase portrait phism Proposition Prove respect restriction Riemannian metric rotation sequence Similarly Smale smooth stable manifold theorem stable set stable summand structurally stable submanifold subspace Suppose taking tangent bundle theory topological conjugacy topological equivalence topological space topologically conjugate trivial uniformly unique unstable vector bundle vector field velocity zero