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Regul. Chaotic Dyn., 2015, Volume 20, Issue 4, Pages 476–485 (Mi rcd27)  

This article is cited in 4 scientific papers (total in 4 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

Funding Agency Grant Number
Office of Naval Research N00014-01-1-076
Ministerio de Economía y Competitividad de España SEV-2011-0087
This research was supported by ONR Grant No. N00014-01-1-0769 and MINECO: ICMAT Severo Ochoa project SEV-2011-0087.


DOI: https://doi.org/10.1134/S1560354715040061

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Bibliographic databases:

MSC: 70H08, 37J40, 53D17
Received: 24.02.2015
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Citation: Alessandro Fortunati, Stephen Wiggins, “A Kolmogorov Theorem for Nearly Integrable Poisson Systems with Asymptotically Decaying Time-dependent Perturbation”, Regul. Chaotic Dyn., 20:4 (2015), 476–485

Citation in format AMSBIB
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\by Alessandro Fortunati, Stephen Wiggins
\paper A Kolmogorov Theorem for Nearly Integrable Poisson Systems with Asymptotically Decaying Time-dependent Perturbation
\jour Regul. Chaotic Dyn.
\yr 2015
\vol 20
\issue 4
\pages 476--485
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. Fortunati, S. Wiggins, “Integrability and strong normal forms for non-autonomous systems in a neighbourhood of an equilibrium”, J. Math. Phys., 57:9 (2016), 092703  crossref  mathscinet  zmath  isi  scopus
    2. A. Fortunati, S. Wiggins, “Normal forms a la Moser for aperiodically time-dependent Hamiltonians in the vicinity of a hyperbolic equilibrium”, Discret. Contin. Dyn. Syst.-Ser. S, 9:4 (2016), 1109–1118  crossref  mathscinet  zmath  isi  scopus
    3. A. Fortunati, S. Wiggins, “Negligibility of small divisor effects in the normal form theory for nearly-integrable Hamiltonians with decaying non-autonomous perturbations”, Celest. Mech. Dyn. Astron., 125:2 (2016), 247–262  crossref  mathscinet  zmath  isi  scopus
    4. A. Fortunati, S. Wiggins, “Transient invariant and quasi-invariant structures in an example of an aperiodically time dependent fluid flow”, Int. J. Bifurcation Chaos, 28:5 (2018), 1830015  crossref  mathscinet  zmath  isi
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