Invariant curves for area preserving maps
This work aims to present tool of this approach is the so-called parameterization method, that produces a Newton-like iterative method to solve the invariance equation for an invariant torus, and the KAM theorem is a result on the convergence of the method. The method was introduced in this setting...
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| Tipo de recurso: | tesis de maestría |
| Fecha de publicación: | 2019 |
| 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:2117/166058 |
| Acceso en línea: | https://hdl.handle.net/2117/166058 |
| Access Level: | acceso abierto |
| Palabra clave: | Differentiable dynamical systems KAM theorem Parameterization Method Newton method Sistemes dinàmics diferenciables Classificació AMS::37 Dynamical systems and ergodic theory::37M Approximation methods and numerical treatment of dynamical systems Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics |
| Sumario: | This work aims to present tool of this approach is the so-called parameterization method, that produces a Newton-like iterative method to solve the invariance equation for an invariant torus, and the KAM theorem is a result on the convergence of the method. The method was introduced in this setting by A. González, À. Jorba, R. de la Llave and J. Villanueva [4] (see A tutorial on KAM theory for preliminary a version). In this work we have followed the review of the method exposed in A parameterizarion method for invariant manifolds. |
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