A lambda-lemma for normally hyperbolic invariant manifolds

TL;DR

This paper extends the classical lambda-lemma to the setting of normally hyperbolic invariant manifolds, providing a new theoretical tool for understanding their dynamics without the compactness assumption.

Contribution

It proves an analogue of the lambda-lemma for normally hyperbolic invariant manifolds, broadening the applicability of this fundamental dynamical systems result.

Findings

Established a lambda-lemma for non-compact normally hyperbolic invariant manifolds

Generalized the classical lambda-lemma to a broader class of invariant manifolds

Provided theoretical foundation for future studies of invariant manifold dynamics

Abstract

Let $N$ be a smooth manifold and $f:N\to N$ be a $C^l$, $l\geq 2$ diffeomorphism. Let $M$ be a normally hyperbolic invariant manifold, not necessarily compact. We prove an analogue of the $\lambda$-lemma in this case.