Shadowing and Hyperbolicity

Lieferzeit: Lieferbar innerhalb 14 Tagen

58,84 

Lecture Notes in Mathematics 2193

ISBN: 3319651838
ISBN 13: 9783319651835
Autor: Pilyugin, Sergei Yu/Sakai, Kazuhiro
Verlag: Springer Verlag GmbH
Umfang: xiv, 218 S., 5 s/w Illustr., 218 p. 5 illus.
Erscheinungsdatum: 02.09.2017
Auflage: 1/2017
Produktform: Kartoniert
Einband: Kartoniert

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.

Artikelnummer: 2608429 Kategorie:

Beschreibung

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

Herstellerkennzeichnung:


Springer Verlag GmbH
Tiergartenstr. 17
69121 Heidelberg
DE

E-Mail: juergen.hartmann@springer.com

Das könnte Ihnen auch gefallen …