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Shadowing and hyperbolicity

Author: Sergei Yu Pilyugin; Kazuhiro Sakai
Publisher: Cham : Springer, 2017.
Series: Lecture notes in mathematics (Springer-Verlag), 2193.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Printed edition:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Sergei Yu Pilyugin; Kazuhiro Sakai
ISBN: 9783319651842 3319651846 3319651838 9783319651835
OCLC Number: 1003290029
Description: 1 online resource (xiv, 218 pages) : illustrations.
Contents: Preface.- 1 Main Definitions and Basic Results --
Lipschitz and H¨older Shadowing and Structural Stability.- 3 C1 interiors of Sets of Systems with Various Shadowing Properties.- 4 Chain Transitive Sets and Shadowing --
References --
Index.
Series Title: Lecture notes in mathematics (Springer-Verlag), 2193.
Responsibility: by Sergei Yu Pilyugin, Kazuhiro Sakai.

Abstract:

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.

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"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. ... Read more...

 
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