Overview
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.
Full Product Details
Author: Sergei Yu Pilyugin ,
Kazuhiro Sakai
Publisher: Springer International Publishing AG
Imprint: Springer International Publishing AG
Edition: 1st ed. 2017
Volume: 2193
Weight: 3.577kg
ISBN: 9783319651835
ISBN 10: 3319651838
Pages: 218
Publication Date: 02 September 2017
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Paperback
Publisher's Status: Active
Availability: Manufactured on demand
We will order this item for you from a manufactured on demand supplier.
Reviews
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)
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 Poetzsche, 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)
