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Commentarii Mathematici Helvetici

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Volume 91, Issue 4, 2016, pp. 653–703
DOI: 10.4171/CMH/399

Published online: 2016-10-24

Nekhoroshev’s estimates for quasi-periodic time-dependent perturbations

Abed Bounemoura[1]

(1) Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil

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.

Keywords: Hamiltonian systems, perturbation theory, effective stability

Bounemoura Abed: Nekhoroshev’s estimates for quasi-periodic time-dependent perturbations. Comment. Math. Helv. 91 (2016), 653-703. doi: 10.4171/CMH/399