Continuation of the exponentially small lower bounds for the splitting of separatrices to a whiskered torus with silver ratio
Document typeExternal research report
Rights accessOpen Access
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.
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