Arnold diffusion in an apriori unstable Hamiltonian system with a non-polynomial perturbation

Gemma Huguet

Departament de Matemātica Aplicada I

Universitat Politecnica de Catalunya, Barcelona

In this talk, I will introduce the problem of global instability for Hamiltonian systems (Arnold' diffusion) and I will describe a geometric mechanism developed by Amadeu Delshams, Rafael de la Llave and Tere M. Seara for detecting global instability in apriori unstable nearly integrable Hamiltonian systems. In [DLS06], this mechanism was applied to overcome the large gap problem in Arnold diffusion for an a priori unstable Hamiltonian system of 2 and 1/2 degrees of freedom, where the perturbation was assumed to be a trigonometric polynomial in the angle variables. I will show that this mechanism also works for a general case of perturbations whose Fourier series in the angle variables do not need to have a finite number of terms, provided that the perturbation is differentiable enough. [DLS06] Amadeu Delshams, Rafael de la Llave, Tere M. Seara, A Geometric Mechanism for Diffusion in Hamiltonian Systems Overcoming the large Gap Problem: Heuristics and Rigorous Verification on a Model, Mem. Amer. Math. Soc., 179(844):1-141, 2006