## Dynamical systems: C.I.M.E. lectures, Bressanone, Italy, June 1978 |

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### Contents

Introduction | 2 |

Hyperbolic sets and homoclinic points | 13 |

Homoclinic classes shadowing lemma and hyperbolic | 25 |

Copyright | |

8 other sections not shown

### Common terms and phrases

algebraic Anosov diffeomorphisms assume bifurcation theory called Cantor set codimension compact consider constant continuous critical point curve defined dense describe differential equations dimensional maps dynamical systems eigenvalues ergodic example Figure finite fixed point follows function furcation geodesic flow given gives group action Hamiltonian homeomorphism Hopf bifurcation hyperbolic periodic point hyperbolic set implies integrable intersection interval invariant coordinate itinerary kneading sequences kneading theory lemma Let f linear Lorenz attractor map f Math measure models neighborhood Newhouse nonwandering set normal form occur open set Palis parameter family periodic orbits periodic points perturbations plane points of f Pol equation population problem proof properties Proposition prove rotation number saddle-node singular points Smale solutions space stable and unstable stable periodic orbits structurally stable submanifold subset symplectic tangent topologically conjugate trajectories transverse turning point unstable manifolds vector field wild hyperbolic set WU(A zero