Shadowing and Hyperbolicity

  • Sergei Yu Pilyugin
  • Kazuhiro Sakai

Part of the Lecture Notes in Mathematics book series (LNM, volume 2193)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Sergei Yu. Pilyugin, Kazuhiro Sakai
    Pages 1-35
  3. Sergei Yu. Pilyugin, Kazuhiro Sakai
    Pages 37-124
  4. Sergei Yu. Pilyugin, Kazuhiro Sakai
    Pages 125-179
  5. Sergei Yu. Pilyugin, Kazuhiro Sakai
    Pages 181-208
  6. Back Matter
    Pages 209-218

About this book

Introduction

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.

Keywords

Dynamical System Pseudotrajectory Shadowing Hyperbolicity Transversality Structural Stability

Authors and affiliations

  • Sergei Yu Pilyugin
    • 1
  • Kazuhiro Sakai
    • 2
  1. 1.Faculty of Mathematics and MechanicsSt. Petersburg State UniversitySt. PetersburgRussia
  2. 2.Faculty of EducationUtsunomiya UniversityUtsunomiyaJapan

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-65184-2
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-65183-5
  • Online ISBN 978-3-319-65184-2
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book