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Regular and Chaotic Dynamics, 2010, Volume 15, Issue 2-3, Pages 159–164
DOI: https://doi.org/10.1134/S156035471002005X (Mi rcd485) 		 
This article is cited in 12 scientific papers (total in 12 papers)

On the 75th birthday of Professor L.P. Shilnikov

Universal dynamics in a neighborhood of a generic elliptic periodic point

V. Gelfreicha, D. Turaevb

a Mathematics Institute, University of Warwick, Zeeman Building, Coventry CV4 7AL, UK
b Imperial College London, South Kensington Campus, London SW7 2AZ, UK
Citations (12)
DOI: https://doi.org/10.1134/S156035471002005X
Abstract: We show that a generic area-preserving two-dimensional map with an elliptic periodic point is $C^\omega$-universal, i.e., its renormalized iterates are dense in the set of all real-analytic symplectic maps of a two-dimensional disk. The results naturally extend onto Hamiltonian and volume-preserving flows.
Keywords: homoclinic tangency, wild hyperbolic set, Newhouse phenomenon, Hamiltonian system, area-preserving map, volume-preserving flow, exponentially small splitting, KAM theory.
Received: 03.11.2009
Accepted: 21.11.2009
Bibliographic databases:
Document Type: Personalia
MSC: 37J40, 37J10, 37C15, 37C20
Language: English
Citation: V. Gelfreich, D. Turaev, “Universal dynamics in a neighborhood of a generic elliptic periodic point”, Regul. Chaotic Dyn., 15:2-3 (2010), 159–164
Citation in format AMSBIB
\Bibitem{GelTur10}
\by V. Gelfreich, D. Turaev
\paper Universal dynamics in a neighborhood of a generic elliptic periodic point
\jour Regul. Chaotic Dyn.
\yr 2010
\vol 15
\issue 2-3
\pages 159--164
\mathnet{http://mi.mathnet.ru/rcd485}
\crossref{https://doi.org/10.1134/S156035471002005X}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2644327}
\zmath{https://zbmath.org/?q=an:1203.37100}
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    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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