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Geometric Theory of Discrete Nonautonomous Dynamical Systems [electronic resource] / by Christian Pȵtzsche.

Por: Pȵtzsche, Christian [author.]Tipo de material: TextoTextoSeries Lecture Notes in Mathematics, 2002Editor: Berlin, Heidelberg : Springer Berlin Heidelberg, 2010Descripción: XXIV, 399p. 17 illus., 2 illus. in color. online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9783642142581Trabajos contenidos: SpringerLink (Online service)Tema(s): Mathematics | Differentiable dynamical systems | Mathematics | Dynamical Systems and Ergodic TheoryFormatos físicos adicionales: Sin títuloClasificación CDD: 515.39 | 515.48 Clasificación LoC:QA313Recursos en línea: de clik aquí para ver el libro electrónico
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Springer eBooksResumen: Nonautonomous dynamical systems provide a mathematical framework for temporally changing phenomena, where the law of evolution varies in time due to seasonal, modulation, controlling or even random effects. Our goal is to provide an approach to the corresponding geometric theory of nonautonomous discrete dynamical systems in infinite-dimensional spaces by virtue of 2-parameter semigroups (processes). These dynamical systems are generated by implicit difference equations, which explicitly depend on time. Compactness and dissipativity conditions are provided for such problems in order to have attractors using the natural concept of pullback convergence. Concerning a necessary linear theory, our hyperbolicity concept is based on exponential dichotomies and splittings. This concept is in turn used to construct nonautonomous invariant manifolds, so-called fiber bundles, and deduce linearization theorems. The results are illustrated using temporal and full discretizations of evolutionary differential equations.
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Nonautonomous Dynamical Systems -- Nonautonomous Difference Equations -- Linear Difference Equations -- Invariant Fiber Bundles -- Linearization.

Nonautonomous dynamical systems provide a mathematical framework for temporally changing phenomena, where the law of evolution varies in time due to seasonal, modulation, controlling or even random effects. Our goal is to provide an approach to the corresponding geometric theory of nonautonomous discrete dynamical systems in infinite-dimensional spaces by virtue of 2-parameter semigroups (processes). These dynamical systems are generated by implicit difference equations, which explicitly depend on time. Compactness and dissipativity conditions are provided for such problems in order to have attractors using the natural concept of pullback convergence. Concerning a necessary linear theory, our hyperbolicity concept is based on exponential dichotomies and splittings. This concept is in turn used to construct nonautonomous invariant manifolds, so-called fiber bundles, and deduce linearization theorems. The results are illustrated using temporal and full discretizations of evolutionary differential equations.

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