This article is cited in 5 papers

A $\lambda$-lemma for Normally Hyperbolic Invariant Manifolds

Jacky Cresson^ab, Stephen Wiggins<sup>c

a</sup> SYRTE, UMR 8630 CNRS, Observatoire de Paris, 77 avenue Denfert-Rochereau, 75014, Paris, France
^b Laboratoire de Mathématiques Appliquées de Pau, UMR CNRS 5142, Université de Pau et des Pays de l’Adour, avenue de l’Université, BP 1155, 64013, Pau Cedex, France
^c School of Mathematics, University of Bristol, University Walk, Bristol, BS8 1TW, UK

Abstract: Let $N$ be a smooth manifold and $f: N \to N$ be a $C^\mathcal{l}, \mathcal{l} \geqslant 2$ diffeomorphism. Let $M$ be a normally hyperbolic invariant manifold, not necessarily compact. We prove an analogue of the $\lambda$-lemma in this case. Applications of this result are given in the context of normally hyperbolic invariant annuli or cylinders which are the basic pieces of all geometric mechanisms for diffusion in Hamiltonian systems. Moreover, we construct an explicit class of three-degree-of-freedom near-integrable Hamiltonian systems which satisfy our assumptions.

Keywords: $\lambda$-lemma, Arnold diffusion, normally hyperbolic manifolds, Moeckel’s mechanism.

MSC: 37-XX, 37Dxx, 37Jxx

Received: 28.11.2014
Accepted: 30.12.2014

Language: English

DOI: 10.1134/S1560354715010074

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