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.
%0 Journal Article
%1 medvedev2013hyperbolic
%A Medvedev, Anton G.
%D 2013
%J Sbornik: Mathematics
%K analysis classical mathematics mechanics physics unread
%N 5
%P 661--682
%R 10.1070/SM2013v204n05ABEH004316
%T Hyperbolic tori in Hamiltonian systems with slowly varying parameter
%V 204
%X 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.
@article{medvedev2013hyperbolic,
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.},
added-at = {2013-07-21T22:12:58.000+0200},
author = {Medvedev, Anton G.},
biburl = {https://www.bibsonomy.org/bibtex/267f2d521eb46dd53fcc4a8e8c5358aca/drmatusek},
doi = {10.1070/SM2013v204n05ABEH004316},
interhash = {9590c13cb6253d08d52fdc83ce13b3a5},
intrahash = {67f2d521eb46dd53fcc4a8e8c5358aca},
journal = {Sbornik: Mathematics},
keywords = {analysis classical mathematics mechanics physics unread},
month = may,
number = 5,
pages = {661--682 },
timestamp = {2013-07-21T22:12:58.000+0200},
title = {Hyperbolic tori in Hamiltonian systems with slowly varying parameter},
volume = 204,
year = 2013
}