Contraction method and Lambda-Lemma

Abstract

We reprove the $\lambda$-Lemma for finite dimensional gradient flows by generalizing the well-known contraction method proof of the local (un)stable manifold theorem. This only relies on the forward Cauchy problem. We obtain a rather quantitative description of (un)stable foliations which allows to equip each leaf with a copy of the flow on the central leaf -- the local (un)stable manifold. These dynamical thickenings are key tools in our recent work [Web]. The present paper provides their construction.

35 pages, 9 figures

References in corpus (4)

• Floer homology and the heat flow
• The Morse-Witten complex via dynamical systems
• Morse homology for the heat flow
• A backward $\lambda$-Lemma for the forward heat flow

Cited by in corpus (1)

• Conley pairs in geometry - Lusternik-Schnirelmann theory and more