## On the existence of invariant sets inside a submanifold convex to a flow |

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### Contents

Preliminary Results | 11 |

The Homology of Asymptotic and Invariant Sets | 18 |

Stability | 28 |

1 other sections not shown

### Common terms and phrases

asymptotic and invariant asymptotic sets bd 7ft canonically conjugate variables Cech cohomology choose a neighborhood closed subset completes the proof continuous function convex with respect coordinate neighborhood cosh cr+(x critical point defined Definition deformation retract denotes the matrix df dT df(q diffeomorphism differential equations dimension energy surface exists a neighborhood flow ijj function f H bd Hamiltonian function Hamiltonian system hence Hk(U Hk(U+ homeomorphic homology homotopic imbedding implies inclusion map isomorphism Jurgen Moser Lemma N(A+ never tangent non-linear open set open subset orbits perturbation proof of Theorem q e R(h r+(x Remark respect to 771 respect to R(h Riemanian sets U+ sinh Sm_1 smooth flow smooth function smooth n-manifold smooth submanifold study the behavior sufficient to show sufficiently small Suppose surface of section tangent to bd thesis topological space topology vector field W(A+ x e bd