## Smooth dynamical systems (Google eBook)Smooth 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 |

246 | |

253 | |

### Common terms and phrases

admissible chart Appendix automorphism Banach space basic set bifurcation called Chapter classiﬁcation 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 ﬁnd ﬁnite dimensional ﬁow ﬂow ﬂow equivalent function given GL(E Hausdorff hence HL(E homeomorphism hyperbolic ﬁxed point hyperbolic linear identiﬁed induced integral curve intersects inverse isomorphism Lemma Let f Liapunov linear automorphism Lipschitz with constant map f map g mapping theorem Morse—Smale non-empty norm open neighbourhood open subset orientation preserving periodic points perturbation phase portrait phism Proposition Prove respect restriction Riemannian metric rotation satisﬁes sequence Similarly 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