This article is cited in 9 papers

A Kolmogorov Theorem for Nearly Integrable Poisson Systems with Asymptotically Decaying Time-dependent Perturbation

Alessandro Fortunati, Stephen Wiggins

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

Abstract: The aim of this paper is to prove the Kolmogorov theorem of persistence of Diophantine flows for nearly integrable Poisson systems associated to a real analytic Hamiltonian with aperiodic time dependence, provided that the perturbation is asymptotically vanishing. The paper is an extension of an analogous result by the same authors for canonical Hamiltonian systems; the flexibility of the Lie series method developed by A. Giorgilli et al. is profitably used in the present generalization.

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

MSC: 70H08, 37J40, 53D17

Received: 24.02.2015

Language: English

DOI: 10.1134/S1560354715040061

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