Shadowing and Hyperbolicity (Paperback, 1st ed. 2017)

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.

General

Imprint:	Springer International Publishing AG
Country of origin:	Switzerland
Series:	Lecture Notes in Mathematics, 2193
Release date:	September 2017
First published:	2017
Authors:	Sergei Yu Pilyugin • Kazuhiro Sakai
Dimensions:	235 x 155 x 15mm (L x W x T)
Format:	Paperback
Pages:	218
Edition:	1st ed. 2017
ISBN-13:	978-3-319-65183-5
Categories:	Books > Science & Mathematics > Mathematics > Applied mathematics > Non-linear science
LSN:	3-319-65183-8
Barcode:	9783319651835

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