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SpringerBriefs in Mathematics

Admissibility and Hyperbolicity

Authors: Barreira, Luís, Dragicevic, Davor, Valls, Claudia

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  • Details the connection between hyperbolicity and admissibility
  • Highlights several applications     
  • Features arguments for exponential contractions
  • Contains useful references for supplementary research
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  • ISBN 978-3-319-90110-7
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Softcover $54.99
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  • ISBN 978-3-319-90109-1
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About this book

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. 


Reviews

“This book gives a comprehensive overview of the relationship between the notions of admissibility and hyperbolicity. … 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.” (Kazuhiro Sakai, zbMATH 1405.37002, 2019)

Table of contents (6 chapters)

Table of contents (6 chapters)

Buy this book

eBook $39.99
price for USA in USD
  • ISBN 978-3-319-90110-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA in USD
  • ISBN 978-3-319-90109-1
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually ready to be dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Admissibility and Hyperbolicity
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG, part of Springer Nature
eBook ISBN
978-3-319-90110-7
DOI
10.1007/978-3-319-90110-7
Softcover ISBN
978-3-319-90109-1
Series ISSN
2191-8198
Edition Number
1
Number of Pages
IX, 145
Topics

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