Hyperbolic tori in Hamiltonian systems with slowly varying parameter

Hyperbolic tori in Hamiltonian systems with slowly varying parameter

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 varie...

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Veröffentlicht in:Sbornik. Mathematics 2013-01, Vol.204 (5), p.661-682
1. Verfasser: Medvedev, A. G.
Format: Artikel
Sprache:eng
Schlagworte:
Constants
fast-slow systems
HAMILTONIANS
hyperbolic tori
KAM-theory
Mathematical analysis
MATHEMATICAL METHODS AND COMPUTING
MATHEMATICAL SOLUTIONS
PERIODICITY
PHASE SPACE
TORI
Toruses
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Beschreibung
Zusammenfassung: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.
ISSN:1064-5616
1468-4802
DOI:10.1070/SM2013v204n05ABEH004316