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Mat. Sb., 2013, Volume 204, Number 5, Pages 45–66 (Mi msb8117)  

Hyperbolic tori in Hamiltonian systems with slowly varying parameter

A. G. Medvedev

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

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.

DOI: https://doi.org/10.4213/sm8117

Full text: PDF file (532 kB)
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English version:
Sbornik: Mathematics, 2013, 204:5, 661–682

Bibliographic databases:

UDC: 517.933
MSC: 37J15, 37J40
Received: 04.03.2012 and 17.12.2012

Citation: A. G. Medvedev, “Hyperbolic tori in Hamiltonian systems with slowly varying parameter”, Mat. Sb., 204:5 (2013), 45–66; Sb. Math., 204:5 (2013), 661–682

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