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An inclination lemma for normally hyperbolic manifolds with an application to diffusion
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Sabbagh, Lara (2015) An inclination lemma for normally hyperbolic manifolds with an application to diffusion. Ergodic Theory and Dynamical Systems, 35 (7). pp. 2269-2291. doi:10.1017/etds.2014.30 ISSN 0143-3857.
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Official URL: http://dx.doi.org/10.1017/etds.2014.30
Abstract
Let (M, Ω) be a smooth symplectic manifold and f:M→M be a symplectic diffeomorphism of class Cl (l⩾3). Let N be a compact submanifold of M which is boundaryless and normally hyperbolic for f. We suppose that N is controllable and that its stable and unstable bundles are trivial. We consider a C1-submanifold Δ of M whose dimension is equal to the dimension of a fiber of the unstable bundle of TNM. We suppose that Δ transversely intersects the stable manifold of N. Then, we prove that for all ε>0, and for n∈N large enough, there exists xn∈N such that fn(Δ) is ε-close, in the C1 topology, to the strongly unstable manifold of xn. As an application of this λ-lemma, we prove the existence of shadowing orbits for a finite family of invariant minimal sets (for which we do not assume any regularity) contained in a normally hyperbolic manifold and having heteroclinic connections. As a particular case, we recover classical results on the existence of diffusion orbits (Arnold’s example).
Item Type: | Journal Article | ||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
Journal or Publication Title: | Ergodic Theory and Dynamical Systems | ||||||
Publisher: | Cambridge University Press | ||||||
ISSN: | 0143-3857 | ||||||
Official Date: | October 2015 | ||||||
Dates: |
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Volume: | 35 | ||||||
Number: | 7 | ||||||
Page Range: | pp. 2269-2291 | ||||||
DOI: | 10.1017/etds.2014.30 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access |
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