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Mosc. Math. J., 2012, Volume 12, Number 4, Pages 705–717 (Mi mmj477)  

This article is cited in 1 scientific paper (total in 1 paper)

On products of skew rotations

M. D. Arnoldab, E. I. Dinaburgac, G. B. Dobrushinaa, S. A. Pirogova, A. N. Rybkoa

a Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Bolshoi Karetny per. 19, Moscow, 127994, Russia
b International Institute of Earthquake Prediction Theory and Mathematical Geophysics of the Russian Academy of Sciences, Profsoyuznaya str., 84/32, Moscow, 117997, Russia
c Schmidt Institute of Physics of the Earth of the Russian Academy of Sciences, B. Gruzinskaya str., 10, Moscow, 123995, Russia

Abstract: Let $\{S_1^t\},\ldots,\{S_n^t\}$ be the one-parametric groups of shifts along the orbits of Hamiltonian systems generated by time-independent Hamiltonians $H_1,\ldots, H_n$ with one degree of freedom. In some problems of population genetics there appear planar transformations having the form $S^{h_n}_n\cdots S_1^{h_1}$ under some conditions on Hamiltonians $H_1,\ldots,H_n$. In this paper we study asymptotical properties of trajectories of such transformations. We show that under classical non-degeneracy condition on the Hamiltonians the trajectories stay in the invariant annuli for generic combinations of lengths $h_1,…, h_n$, while for the special case $h_1+…+h_n=0$ there exists a trajectory escaping to infinity.

Key words and phrases: KAM theory, Hamiltonian systems.

Full text: http://www.mathjournals.org/.../2012-012-004-003.html
References: PDF file   HTML file

Bibliographic databases:

Document Type: Article
MSC: 37J40, 37J15, 37M05
Received: July 13, 2011
Language: English

Citation: M. D. Arnold, E. I. Dinaburg, G. B. Dobrushina, S. A. Pirogov, A. N. Rybko, “On products of skew rotations”, Mosc. Math. J., 12:4 (2012), 705–717

Citation in format AMSBIB
\Bibitem{ArnDinDob12}
\by M.~D.~Arnold, E.~I.~Dinaburg, G.~B.~Dobrushina, S.~A.~Pirogov, A.~N.~Rybko
\paper On products of skew rotations
\jour Mosc. Math.~J.
\yr 2012
\vol 12
\issue 4
\pages 705--717
\mathnet{http://mi.mathnet.ru/mmj477}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3076851}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000314341500003}


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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. Arnold M., Zharnitsky V., “Pinball Dynamics: Unlimited Energy Growth in Switching Hamiltonian Systems”, Commun. Math. Phys., 338:2 (2015), 501–521  crossref  mathscinet  zmath  isi  elib  scopus
  • Moscow Mathematical Journal
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