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Shadowing and hyperbolicity

Pilyugin, Sergei Yu.

Shadowing and hyperbolicity

Record Type:	Electronic resources : Monograph/item
Title/Author:	Shadowing and hyperbolicityby Sergei Yu. Pilyugin, Kazuhiro Sakai.
Author:	Pilyugin, Sergei Yu.
other author:	Sakai, Kazuhiro.
Published:	Cham :Springer International Publishing :2017.
Description:	xiv, 218 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Shadowing (Differentiable dynamical systems)
Online resource:	http://dx.doi.org/10.1007/978-3-319-65184-2
ISBN:	9783319651842$q(electronic bk.)

Shadowing and hyperbolicity
Pilyugin, Sergei Yu.

Shadowing and hyperbolicity[electronic resource] /by Sergei Yu. Pilyugin, Kazuhiro Sakai. - Cham :Springer International Publishing :2017. - xiv, 218 p. :ill., digital ;24 cm. - Lecture notes in mathematics,21930075-8434 ;. - Lecture notes in mathematics ;2035..

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.

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.

ISBN: 9783319651842$q(electronic bk.)

Standard No.: 10.1007/978-3-319-65184-2doiSubjects--Topical Terms:

199017
Shadowing (Differentiable dynamical systems)

LC Class. No.: QA614.84

Dewey Class. No.: 515.352

Shadowing and hyperbolicity
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520 $a 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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