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Sbornik: Mathematics, 2013, Volume 204, Issue 5, Pages 661–682
DOI: https://doi.org/10.1070/SM2013v204n05ABEH004316 (Mi sm8117) 		 
Hyperbolic tori in Hamiltonian systems with slowly varying parameter

A. G. Medvedev

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (338 kB) Russian version article
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DOI: https://doi.org/10.1070/SM2013v204n05ABEH004316
Abstract: This paper looks at a Hamiltonian system which depends periodically on a parameter. For each value of the parameter the system is assumed to have a hyperbolic periodic solution. Using the methods in KAM-theory it is proved that if the Hamiltonian is perturbed so that the value of the parameter varies with constant small frequency, then the nonautonomous system will have hyperbolic 2-tori in the extended phase space.
Bibliography: 12 titles.
Keywords: KAM-theory, hyperbolic tori, fast-slow systems.
Received: 04.03.2012 and 17.12.2012
Bibliographic databases:
Document Type: Article
UDC: 517.933
MSC: 37J15, 37J40
Language: English
Original paper language: Russian
Citation: A. G. Medvedev, “Hyperbolic tori in Hamiltonian systems with slowly varying parameter”, Sb. Math., 204:5 (2013), 661–682
Citation in format AMSBIB
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