Exponentially small lower bounds for the splitting of separatrices to whiskered tori with frequencies of constant type
We study the splitting of invariant manifolds of whiskered tori with two frequencies in nearlyintegrable Hamiltonian systems, such that the hyperbolic part is given by a pendulum. We consider a 2-dimensional torus with a fast frequency vector $\omega/v\epsilon$, with $\epsilon=(1,\Omega)$ where $\Om...
| Autores: | , , |
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| Tipo de documento: | relatório científico |
| Data de publicação: | 2014 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositório: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglês |
| OAI Identifier: | oai:upcommons.upc.edu:2117/22687 |
| Acesso em linha: | https://hdl.handle.net/2117/22687 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Hamiltonian systems splitting of separatrices Melnikov integrals numbers of constant type Equacions diferencials ordinàries Sistemes dinàmics diferenciables Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Resumo: | We study the splitting of invariant manifolds of whiskered tori with two frequencies in nearlyintegrable Hamiltonian systems, such that the hyperbolic part is given by a pendulum. We consider a 2-dimensional torus with a fast frequency vector $\omega/v\epsilon$, with $\epsilon=(1,\Omega)$ where $\Omega$ is an irrational number of constant type, i.e. a number whose continued fraction has bounded entries. Applying the Poincar´e–Melnikov method, we find exponentially small lower bounds for the maximal splitting distance between the stable and unstable invariant manifolds associated to the invariant torus, and we show that these bounds depend strongly on the arithmetic properties of the frequencies. |
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