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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Detalles Bibliográficos
Autor: Wang, Chanyan
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
Descripción
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.