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Regul. Chaotic Dyn., 2015, Volume 20, Issue 1, Pages 94–108 (Mi rcd63)  

This article is cited in 1 scientific paper (total in 1 paper)

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

Jacky Cressonab, Stephen Wigginsc

a 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

Funding Agency Grant Number
Office of Naval Research N00014-01-1-076
SW would like to acknowledge the support of ONR Grant No. N00014-01-1-0769.


DOI: https://doi.org/10.1134/S1560354715010074

References: PDF file   HTML file

Bibliographic databases:

MSC: 37-XX, 37Dxx, 37Jxx
Received: 28.11.2014
Accepted:30.12.2014
Language:

Citation: Jacky Cresson, Stephen Wiggins, “A $\lambda$-lemma for Normally Hyperbolic Invariant Manifolds”, Regul. Chaotic Dyn., 20:1 (2015), 94–108

Citation in format AMSBIB
\Bibitem{CreWig15}
\by Jacky Cresson, Stephen Wiggins
\paper A $\lambda$-lemma for Normally Hyperbolic Invariant Manifolds
\jour Regul. Chaotic Dyn.
\yr 2015
\vol 20
\issue 1
\pages 94--108
\mathnet{http://mi.mathnet.ru/rcd63}
\crossref{https://doi.org/10.1134/S1560354715010074}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3304940}
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    This publication is cited in the following articles:
    1. Teramoto H., Toda M., Takahashi M., Kono H., Komatsuzaki T., “Mechanism and Experimental Observability of Global Switching Between Reactive and Nonreactive Coordinates At High Total Energies”, Phys. Rev. Lett., 115:9 (2015), 093003  crossref  isi  scopus
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