Continuation of the exponentially small transversality for the splitting of separatrices to a whiskered torus with silver ratio

Cita com:
hdl:2117/27844
Document typeArticle
Defense date2014-11
PublisherSpringer
Rights accessOpen Access
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Abstract
We study the exponentially small splitting of invariant manifolds of whiskered
(hyperbolic) tori with two fast frequencies in nearly integrable Hamiltonian systems whose
hyperbolic part is given by a pendulum. We consider a torus whose frequency ratio is the silver
number Ω =
√
2
−
1. We show that the Poincar ́
e – Melnikov method can be applied to establish
the existence of 4 transverse homoclinic orbits to the whiskered torus, and provide asymptotic
estimates for the transversality of the splitting
whose dependence on the perturbation parameter
ε
satisfies a periodicity property. We also prove
the continuation of the transversality of the
homoclinic orbits for all the sufficiently small values of
ε
, generalizing the results previously
known for the golden number
CitationDelshams, A.; Gonchenko, M.; Gutiérrez, P. Continuation of the exponentially small transversality for the splitting of separatrices to a whiskered torus with silver ratio. "Regular and chaotic dynamics", Novembre 2014, vol. 19, núm. 6, p. 663-680.
ISSN1560-3547
Publisher versionhttp://link.springer.com/article/10.1134/S1560354714060057
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