A λ-lemma for Normally Hyperbolic Invariant Manifolds

Jacky Cresson, Stephen R Wiggins

Research output: Contribution to journalArticle (Academic Journal)

2 Citations (Scopus)
264 Downloads (Pure)

Abstract

Let N be a smooth manifold and f: NN be a C , ⩾ 2 diffeomorphism. Let M be a normally hyperbolic invariant manifold, not necessarily compact. We prove an analogue of the λ-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.
Original languageEnglish
Pages (from-to)94-108
Number of pages15
JournalRegular and Chaotic Dynamics
Volume20
Issue number1
DOIs
Publication statusPublished - Jan 2015

Keywords

  • 37-XX
  • 37Dxx
  • 37Jxx
  • λ-lemma
  • Arnold diffusion
  • normally hyperbolic manifolds
  • Moeckel’s mechanism

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