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2016 Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders
Patrick Bernard, Vadim Kaloshin, Ke Zhang
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Acta Math. 217(1): 1-79 (2016). DOI: 10.1007/s11511-016-0141-5

Abstract

We prove a form of Arnold diffusion in the a-priori stable case. Let H0(p)+ϵH1(θ,p,t),θTn,pBn,tT=R/T,be a nearly integrable system of arbitrary degrees of freedom n2 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.

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Patrick Bernard. Vadim Kaloshin. Ke Zhang. "Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders." Acta Math. 217 (1) 1 - 79, 2016. https://doi.org/10.1007/s11511-016-0141-5

Information

Received: 4 April 2013; Revised: 28 September 2016; Published: 2016
First available in Project Euclid: 22 February 2017

zbMATH: 1368.37068
MathSciNet: MR3646879
Digital Object Identifier: 10.1007/s11511-016-0141-5

Rights: 2017 © Institut Mittag-Leffler

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