Moscow Mathematical Journal

Volume 14, Issue 2, April–June 2014 pp. 181–203.

Generic Fast Diffusion for a Class of Non-Convex Hamiltonians with Two Degrees of Freedom

Authors: Abed Bounemoura (1) and Vadim Kaloshin (2)
Author institution:(1) Université Paris Dauphine, CEREMADE, Place du Marchal de Lattre de Tassigny
(2) Department of Mathematics, University of Maryland, College Park, MD, 20817

Summary:

In this paper, we study small perturbations of a class of non-convex integrable Hamiltonians with two degrees of freedom, and we prove a result of diffusion for an open and dense set of perturbations, with an optimal time of diffusion which grows linearly with respect to the inverse of the size of the perturbation.

2010 Mathematics Subject Classification. 37J40.

Keywords: Arnold diffusion, linear diffusion, superconductivity channels, Nekhoroshev theory, convexity, resonant normal forms.

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