MiS Preprint Repository

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 $C^1$-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.