Nekhoroshev’s estimates for quasi-periodic time-dependent perturbations
Abed Bounemoura
Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil
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Abstract
In this paper, we consider a Diophantine quasi-periodic time-dependent analytic perturbation of a convex integrable Hamiltonian system, and we prove a result of stability of the action variables for an exponentially long interval of time. This extends known results for periodic time-dependent perturbations, and partly solves a long standing conjecture of Chirikov and Lochak. We also obtain improved stability estimates close to resonances or far away from resonances, and a more general result without any Diophantine condition.
Cite this article
Abed Bounemoura, Nekhoroshev’s estimates for quasi-periodic time-dependent perturbations. Comment. Math. Helv. 91 (2016), no. 4, pp. 653–703
DOI 10.4171/CMH/399