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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Bibliographic Information

Book Title: Shadowing in Dynamical Systems
Authors: Sergei Yu. Pilyugin
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/BFb0093184
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1999
Softcover ISBN: 978-3-540-66299-0Published: 17 September 1999
eBook ISBN: 978-3-540-48429-5Published: 14 November 2006
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XX, 276
Topics: Global Analysis and Analysis on Manifolds, Dynamical Systems and Ergodic Theory

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Table of contents (4 chapters)

Front Matter

Shadowing near an invariant set

Topologically stable, structurally stable, and generic systems

Systems with special structure

Numerical applications of shadowing

Back Matter

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