A lambda-lemma for normally hyperbolic invariant manifolds

Jacky Cresson (1) , Stephen Wiggins (2)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 School of Mathematics [Bristol]

Let $N$ be a smooth manifold and $f:N\rightarrow N$ 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.

Mots clés: lambda-lemma; normally hyperbolic manifolds; Hamiltonian systems; Arnold diffusion

Domaines: Systèmes dynamiques [math.DS]

Jacky Cresson, Stephen Wiggins. A lambda-lemma for normally hyperbolic invariant manifolds. 2005. ⟨hal-00012889⟩