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Continuation of the exponentially small lower bounds 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 typeResearch report
Defense date2014-09
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 $\Omega=\sqrt2-1$. We show that the oincare-Melnikov method can be applied to establish the existence of 4 transverse homoclinic orbits to the whiskered torus, and provide asymptotic estimates for the tranversality of the splitting whose dependence on the perturbation parameter $\varepsilon$ satisffies a periodicity property. We also prove the continuation of the transversality of the homoclinic orbits for all the sufficiently small values of $\varepsilon
CitationDelshams, A.; Gonchenko, M.; Gutiérrez, P. "Continuation of the exponentially small lower bounds for the splitting of separatrices to a whiskered torus with silver ratio". 2014. 
Is part of[prepr201404DelGG]
URIhttp://hdl.handle.net/2117/24138
URL other repositoryhttp://www.ma1.upc.edu/recerca/preprints/preprints-2014/preprint-2014
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