A KAM theorem without action-angle variables for elliptic lower dimensional tori
We study elliptic lower dimensional invariant tori of Hamiltonian systems via parameterizations. The method is based in solving iteratively the functional equations that stand for invariance and reducibility. In contrast with classical methods, we do not assume that the system is close to integrable...
| Autores: | , |
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| Tipo de recurso: | informe técnico |
| Fecha de publicación: | 2010 |
| 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:2117/7067 |
| Acceso en línea: | https://hdl.handle.net/2117/7067 |
| Access Level: | acceso abierto |
| Palabra clave: | Hamiltonian systems Elliptic invariant tori KAM theory Parameterization methods Hamilton, Sistemes de Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics |
| Sumario: | We study elliptic lower dimensional invariant tori of Hamiltonian systems via parameterizations. The method is based in solving iteratively the functional equations that stand for invariance and reducibility. In contrast with classical methods, we do not assume that the system is close to integrable nor that is written in action-angle variables. We only require an approximation of an invariant torus of fixed vector of basic frequencies and a basis along the torus that approximately reduces the normal variational equations to constant coefficients. We want to highlight that this approach presents many advantages compared with methods which are built in terms of canonical transformations, e.g., it produces simpler and more constructive proofs that lead to more efficient numerical algorithms for the computation of these objects. Such numerical algorithms are suitable to be adapted in order to perform computer ssisted proofs. |
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