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Admissibility and Hyperbolicity

  • Luís Barreira
  • Davor Dragičević
  • Claudia Valls

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Luís Barreira, Davor Dragičević, Claudia Valls
    Pages 1-10
  3. Luís Barreira, Davor Dragičević, Claudia Valls
    Pages 11-32
  4. Luís Barreira, Davor Dragičević, Claudia Valls
    Pages 33-54
  5. Luís Barreira, Davor Dragičević, Claudia Valls
    Pages 55-74
  6. Luís Barreira, Davor Dragičević, Claudia Valls
    Pages 75-106
  7. Luís Barreira, Davor Dragičević, Claudia Valls
    Pages 107-137
  8. Back Matter
    Pages 139-145

About this book

Introduction

This book gives a comprehensive overview of the relationship between admissibility and hyperbolicity. Essential theories and selected developments are discussed with highlights to applications. The dedicated readership includes researchers and graduate students specializing in differential equations and dynamical systems (with emphasis on hyperbolicity) who wish to have a broad view of the topic and working knowledge of its techniques. The book may also be used as a basis for appropriate graduate courses on hyperbolicity; the pointers and references given to further research will be particularly useful.

The material is divided into three parts: the core of the theory, recent developments, and applications. The first part pragmatically covers the relation between admissibility and hyperbolicity, starting with the simpler case of exponential contractions. It also considers exponential dichotomies, both for discrete and continuous time, and establishes corresponding results building on the arguments for exponential contractions. The second part considers various extensions of the former results, including a general approach to the construction of admissible spaces and the study of nonuniform exponential behavior. Applications of the theory to the robustness of an exponential dichotomy, the characterization of hyperbolic sets in terms of admissibility, the relation between shadowing and structural stability, and the characterization of hyperbolicity in terms of Lyapunov sequences are given in the final part. 

Keywords

Exponential Dichotomies Perron hyperbolicity admissibility dynamical systems differential equations Sequences of linear operators linear operators Nonuniqueness of solutions Robustness of hyperbolicity Lyapunov sequences Nonuniform Hyperbolicity Nonuniqueness of Solutions Admissible Spaces Robustness of Hyperbolicity Hyperbolic Sets Shadowing Property

Authors and affiliations

  • Luís Barreira
    • 1
  • Davor Dragičević
    • 2
  • Claudia Valls
    • 3
  1. 1.Departamento de Matemática, Instituto Superior TécnicoUniversidade de LisboaLisboaPortugal
  2. 2.Department of MathematicsUniversity of RijekaRijekaCroatia
  3. 3.Departamento de Matemática, Instituto Superior TécnicoUniversidade de LisboaLisboaPortugal

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-90110-7
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-90109-1
  • Online ISBN 978-3-319-90110-7
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • Buy this book on publisher's site