Geodesic
Hyperbolic tori in Hamiltonian systems with slowly varying parameter
Sbornik. Mathematics, Tome 204 (2013) no. 5, pp. 661-682

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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. 
@article{SM_2013_204_5_a2,
     author = {A. G. Medvedev},
     title = {Hyperbolic tori in {Hamiltonian} systems with slowly varying parameter},
     journal = {Sbornik. Mathematics},
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     publisher = {mathdoc},
     volume = {204},
     number = {5},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2013_204_5_a2/}
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A. G. Medvedev. Hyperbolic tori in Hamiltonian systems with slowly varying parameter. Sbornik. Mathematics, Tome 204 (2013) no. 5, pp. 661-682. http://geodesic.mathdoc.fr/item/SM_2013_204_5_a2/