Geometric Theory of Discrete Nonautonomous Dynamical Systems / by Christian Pötzsche.

Format:

Book

Author/Creator:

Pötzsche, Christian, author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 2002.

Lecture Notes in Mathematics, 0075-8434 ; 2002

Language:

English

Subjects (All):

Differentiable dynamical systems.

Dynamical Systems and Ergodic Theory.

Local Subjects:

Dynamical Systems and Ergodic Theory.

Physical Description:

1 online resource (XXIV, 399 pages 17 illustrations, 2 illustrations in color).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg, 2010.

System Details:

text file PDF

Summary:

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.

Contents:

Nonautonomous Dynamical Systems

Nonautonomous Difference Equations

Linear Difference Equations

Invariant Fiber Bundles

Linearization.

Other Format:

Printed edition:

ISBN:

9783642142581

Access Restriction:

Restricted for use by site license.