Pilyugin / Sakai Shadowing and Hyperbolicity

1. Auflage 2017
ISBN: 978-3-319-65184-2
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 2193, 218 Seiten, eBook

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Pilyugin, Sergei Yu

Sakai, Kazuhiro

Inhaltsverzeichnis

Preface.- 1 Main De?nitions 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.