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Lecture Notes in Mathematics

Shadowing and Hyperbolicity

Authors: Pilyugin, Sergei Yu, Sakai, Kazuhiro

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  • Provides a survey of current research and new approaches in the theory of shadowing of approximate trajectories of dynamical systems
  • Contains novelty approach for proving hyperbolicity by using the sifting method of Liao,  which is both powerful and self-contained 
  • A main feature is the direct, straightforward approach to the results, well written, in an easy-to-read, comfortable pace
  • Can be used right after a course of introduction to dynamical systems or even hyperbolic dynamics
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eBook 42,79 €
price for Spain (gross)
  • ISBN 978-3-319-65184-2
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 51,99 €
price for Spain (gross)
  • ISBN 978-3-319-65183-5
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this book

Focusing on the theory of shadowing of approximate trajectories (pseudotrajectories) of dynamical systems, this book surveys recent progress in establishing relations between shadowing and such basic notions from the classical theory of structural stability as hyperbolicity and transversality.

Special attention is given to the study of "quantitative" shadowing properties, such as Lipschitz shadowing (it is shown that this property is equivalent to structural stability both for diffeomorphisms and smooth flows), and to the passage to robust shadowing (which is also equivalent to structural stability in the case of diffeomorphisms, while the situation becomes more complicated in the case of flows).

Relations between the shadowing property of diffeomorphisms on their chain transitive sets and the hyperbolicity of such sets are also described.

The book will allow young researchers in the field of dynamical systems to gain a better understanding of new ideas in the global qualitative theory. It will also be of interest to specialists in dynamical systems and their applications.

Reviews

“The book is clearly written and appropriate both for advanced graduate students in the area and for researchers working or being interested in the field.” (Christian Pötzsche, zbMATH 1426.37004, 2020)
“This book gives an up-to-date account of results on the relations between shadowing and such basic notions from the classical theory of structural stability as hyperbolicity and transversality. … The style of presentation is very clear and, in my opinion, the book is quite suitable for researchers in the field of dynamical systems to understand the global qualitative theory from different points of view.” (Yujun Zhu, Mathematical Reviews, July, 2018)

Table of contents (4 chapters)

Table of contents (4 chapters)

Buy this book

eBook 42,79 €
price for Spain (gross)
  • ISBN 978-3-319-65184-2
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 51,99 €
price for Spain (gross)
  • ISBN 978-3-319-65183-5
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Shadowing and Hyperbolicity
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2193
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-65184-2
DOI
10.1007/978-3-319-65184-2
Softcover ISBN
978-3-319-65183-5
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XIV, 218
Number of Illustrations
5 b/w illustrations
Topics

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