Shadowing in Dynamical Systems

Sergei Yu. Pilyugin (auth.)3540662995, 9783540662990

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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Table of contents :
Shadowing near an invariant set….Pages 1-101
Topologically stable, structurally stable, and generic systems….Pages 103-172
Systems with special structure….Pages 173-217
Numerical applications of shadowing….Pages 219-257