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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.