TY  - BOOK
AU  - Pilyugin,Sergei Yu
AU  - Sakai,Kazuhiro
ED  - SpringerLink (Online service)
TI  - Shadowing and Hyperbolicity
T2  - Lecture Notes in Mathematics,
SN  - 9783319651842
AV  - QA313 
U1  - 515.39 23
PY  - 2017///
CY  - Cham
PB  - Springer International Publishing, Imprint: Springer
KW  - Dynamics
KW  - Ergodic theory
KW  - Dynamical Systems and Ergodic Theory
N1  - 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
N2  - 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
UR  - https://doi.org/10.1007/978-3-319-65184-2
ER  -