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Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders

Bernard, Patrick; Kaloshin, Vadim; Zhang, K. (2017), Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders, Acta Mathematica, 217, 1, p. 1-79. 10.1007/s11511-016-0141-5

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Type
Article accepté pour publication ou publié
Date
2017
Journal name
Acta Mathematica
Volume
217
Number
1
Publisher
F. & G. Beijer
Pages
1-79
Publication identifier
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Author(s)
Bernard, Patrick cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Kaloshin, Vadim

Zhang, K. cc
Abstract (EN)
We prove a form of Arnold diffusion in the a-priori stable case. LetH0(p)+ϵH1(θ,p,t),θ∈Tn,p∈Bn,t∈T=R/T,be a nearly integrable system of arbitrary degrees of freedom n⩾2 with a strictly convex H0. We show that for a “generic” ϵH1, there exists an orbit (θ,p) satisfying∥p(t)−p(0)∥>l(H1)>0,where l(H1) is independent of ϵ. The diffusion orbit travels along a codimension-1 resonance, and the only obstruction to our construction is a finite set of additional resonances.For the proof we use a combination of geometric and variational methods, and manage to adapt tools which have recently been developed in the a-priori unstable case.
Subjects / Keywords
Arnold diffusion