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Shadowing in Dynamical Systems

  • Book
  • © 1999

Overview

Authors:
  1. Sergei Yu. Pilyugin
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1706)

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Table of contents (4 chapters)

  1. Front Matter

    Pages I-XVII
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  2. Shadowing near an invariant set

    • Sergei Yu. Pilyugin
    Pages 1-101

  3. Topologically stable, structurally stable, and generic systems

    • Sergei Yu. Pilyugin
    Pages 103-172

  4. Systems with special structure

    • Sergei Yu. Pilyugin
    Pages 173-217

  5. Numerical applications of shadowing

    • Sergei Yu. Pilyugin
    Pages 219-257

  6. Back Matter

    Pages 259-271
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Keywords

About this book

This book is an introduction to the theory of shadowing of approximate trajectories in dynamical systems by exact ones. This is the first book completely devoted to the theory of shadowing. It shows the importance of shadowing theory for both the qualitative theory of dynamical systems and the theory of numerical methods. Shadowing Methods allow us to estimate differences between exact and approximate solutions on infinite time intervals and to understand the influence of error terms. The book is intended for specialists in dynamical systems, for researchers and graduate students in the theory of numerical methods.

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