RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Regul. Chaotic Dyn.: Year: Volume: Issue: Page: Find

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

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

References: PDF file   HTML file

Bibliographic databases:

MSC: 70H08, 37J40, 53D17
Language:

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
\Bibitem{ForWig15} \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 \mathnet{http://mi.mathnet.ru/rcd27} \crossref{https://doi.org/10.1134/S1560354715040061} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3376603} \zmath{https://zbmath.org/?q=an:06507837} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2015RCD....20..476F} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000358990500006} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84938635704} 

• http://mi.mathnet.ru/eng/rcd27
• http://mi.mathnet.ru/eng/rcd/v20/i4/p476

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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
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
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
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