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This article is cited in 12 scientific papers (total in 12 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.
Received: 07.05.2014 Accepted: 05.09.2014
Citation:
Alessandro Fortunati, Stephen Wiggins, “Persistence of Diophantine Flows for Quadratic Nearly Integrable Hamiltonians under Slowly Decaying Aperiodic Time Dependence”, Regul. Chaotic Dyn., 19:5 (2014), 586–600
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https://www.mathnet.ru/eng/rcd184 https://www.mathnet.ru/eng/rcd/v19/i5/p586
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Abstract page: | 197 | References: | 37 |
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