Preprint 24/2004

On hyperbolic vectorfields on stratified spaces

Ursula Ludwig

Contact the author: Please use for correspondence this email.
Submission date: 27. Apr. 2004
Pages: 18
MSC-Numbers: 57R70, 58A35
Keywords and phrases: stratified spaces, normal hyperbolicity
Download full preprint: PDF (597 kB), PS ziped (192 kB)

The goal of this article is twofold. First, we want to generalize the stable/unstable manifold theorem for a normal hyperbolic invariant set to the situation where we have only Lipschitz conditions instead of formula3-smoothness assumptions. This was already claimed in the book of Hirsch/Shub/Pugh but not worked out. We will need the notion of a generalized Jacobian as well as the Implicit Function Theorem with Lipschitz conditions introduced by Clarke. Second, we apply this result to give a good generalization of the notion of a hyperbolic fixed point to a stratified vectorfield on a stratified space.

03.04.2017, 12:08