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

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Delshams Valdés, AmadeuMés informacióMés informacióMés informació
Gonchenko, Marina
Gutiérrez Serrés, PereMés informacióMés informació
Document typeArticle
Defense date2014-11
PublisherSpringer
Rights accessOpen Access
Attribution-NonCommercial-NoDerivs 3.0 Spain
This work is protected by the corresponding intellectual and industrial property rights. Except where otherwise noted, its contents are licensed under a Creative Commons license : Attribution-NonCommercial-NoDerivs 3.0 Spain
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. 
URIhttp://hdl.handle.net/2117/27844
DOI10.1134/S1560354714060057
ISSN1560-3547
Publisher versionhttp://link.springer.com/article/10.1134/S1560354714060057
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