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Seminários do IMPA

Sistemas Dinâmicos

Normally hyperbolic invariant manifolds: noncompactness and geometry
Jaap Eldering

Imperial college
Quarta-feira, 2 de abril de 2014, 15:30
Sala 236

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.