This article is cited in 14 papers

Persistence of Diophantine Flows for Quadratic Nearly Integrable Hamiltonians under Slowly Decaying Aperiodic Time Dependence

Alessandro Fortunati, Stephen Wiggins

School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom

Abstract: The aim of this paper is to prove a Kolmogorov type result for a nearly integrable Hamiltonian, quadratic in the actions, with an aperiodic time dependence. The existence of a torus with a prefixed Diophantine frequency is shown in the forced system, provided that the perturbation is real-analytic and (exponentially) decaying with time. The advantage consists in the possibility to choose an arbitrarily small decaying coefficient consistently with the perturbation size.
The proof, based on the Lie series formalism, is a generalization of a work by A. Giorgilli.

Keywords: Hamiltonian systems, Kolmogorov theorem, aperiodic time dependence.

MSC: 70H08, 37J40, 37J25

Received: 07.05.2014
Accepted: 05.09.2014

Language: English

DOI: 10.1134/S1560354714050062

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