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The parameterization method for invariant manifolds III: overview and applications
Cabré Vilagut, Xavier; Fontich i Julià, Ernest; Llave Canosa, Rafael de la
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
We describe a method to establish existence and regularity of invariant manifolds and, at the same time to find simple maps which are conjugated to the dynamics on them. The method establishes several invariant manifold theorems. For instance, it reduces the proof of the usual stable manifold theorem near hyperbolic points to an application of the implicit function theorem in Banach spaces. We also present several other applications of the method.
Differentiable dynamical systems
invariant manifolds
Sistemes dinàmics diferenciables
Teoria ergòdica
Classificació AMS::37 Dynamical systems and ergodic theory::37D Dynamical systems with hyperbolic behavior
Classificació AMS::37 Dynamical systems and ergodic theory::37M Approximation methods and numerical treatment of dynamical systems
Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
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