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Geometric Theory of Discrete Nonautonomous Dynamical Systems

  • Christian Pötzsche

Part of the Lecture Notes in Mathematics book series (LNM, volume 2002)

Table of contents

  1. Front Matter
    Pages i-xxiv
  2. Christian Pötzsche
    Pages 1-36
  3. Christian Pötzsche
    Pages 37-94
  4. Christian Pötzsche
    Pages 95-185
  5. Christian Pötzsche
    Pages 187-316
  6. Christian Pötzsche
    Pages 317-343
  7. Back Matter
    Pages 345-405

About this book

Introduction

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.

Keywords

Exponential dichotomy Invariant fiber bundles Nonautonomous difference equations Nonautonomous dynamical systems Topological linearization difference equation dynamical systems

Authors and affiliations

  • Christian Pötzsche
    • 1
  1. 1.Centre for Mathematical SciencesMunich University of TechnologyGarchingGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-14258-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 2010
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-14257-4
  • Online ISBN 978-3-642-14258-1
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site
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