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|Type:||Artigo de periódico|
|Title:||A Backward λ-lemma For The Forward Heat Flow|
|Abstract:||The inclination or λ-lemma is a fundamental tool in finite dimensional hyperbolic dynamics. In contrast to finite dimension, we consider the forward semi-flow on the loop space of a closed Riemannian manifold M provided by the heat flow. The main result is a backward λ-lemma for the heat flow near a hyperbolic fixed point x. There are the following novelties. Firstly, infinite versus finite dimension. Secondly, semi-flow versus flow. Thirdly, suitable adaption provides a new proof in the finite dimensional case. Fourthly and a priori most surprisingly, our λ-lemma moves the given disk transversal to the unstable manifold backward in time, although there is no backward flow. As a first application we propose a new method to calculate the Conley homotopy index of x. © 2014 Springer-Verlag Berlin Heidelberg.|
|Editor:||Springer New York LLC|
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
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