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Seminários do IMPA

Sistemas Dinâmicos

Título |
Normally hyperbolic invariant manifolds: noncompactness and geometry |

Expositor |
Jaap Eldering
Imperial college |

Data |
Quarta-feira, 2 de abril de 2014, 15:30 |

Local |
Sala 236 |

Resumo |

As generalization of hyperbolic fixed points, normally hyperbolic

invariant manifolds (NHIMs for short) are an important tool to

globally study perturbations of dynamical systems.

In this talk, I will first briefly review the theory of NHIMs and

their use in applications. Then I will formulate the theorem on

persistence of NHIMs and show how my result generalizes the classical

compact to a noncompact differential geometric setting.

Noncompactness requires us to introduce the concept of Riemannian

manifolds of bounded geometry. These can be viewed as the class of

uniformly C^k manifolds; I will illustrate this concept with images.

Finally, I will describe why bounded geometry is needed and say

a few words about how it enters the proof of persistence of NHIMs.