Continuation of the exponentially small lower bounds for the splitting of separatrices to a whiskered torus with silver ratio
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...
| Autores: | , , |
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| Tipo de recurso: | informe técnico |
| Fecha de publicación: | 2014 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/24138 |
| Acceso en línea: | https://hdl.handle.net/2117/24138 |
| Access Level: | acceso abierto |
| Palabra clave: | Invariant manifolds transverse homoclinic orbits splitting of separatrices Melnikov integrals silver ratio Sistemes dinàmics diferenciables Equacions diferencials ordinàries Varietats diferenciables Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | 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 |
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