Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

A λ-lemma for normally hyperbolic invariant manifolds

A λ-lemma for normally hyperbolic invariant manifolds Let N be a smooth manifold and f: N → N be a C ℓ , ℓ ⩾ 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Regular and Chaotic Dynamics Springer Journals

A λ-lemma for normally hyperbolic invariant manifolds

Loading next page...
 
/lp/springer-journals/a-lemma-for-normally-hyperbolic-invariant-manifolds-usaQ0COCNq

References (42)

Publisher
Springer Journals
Copyright
Copyright © 2015 by Pleiades Publishing, Ltd.
Subject
Mathematics; Dynamical Systems and Ergodic Theory
ISSN
1560-3547
eISSN
1468-4845
DOI
10.1134/S1560354715010074
Publisher site
See Article on Publisher Site

Abstract

Let N be a smooth manifold and f: N → N be a C ℓ , ℓ ⩾ 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.

Journal

Regular and Chaotic DynamicsSpringer Journals

Published: Feb 1, 2015

There are no references for this article.