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Summary:

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.

Table of Contents:

• 1. Introduction
• 2. Exponential Contractions
• 3. Exponential Dichotomies: Discrete Time
• 4. Exponential Dichotomies: Continuous Time
• 5. Admissibility: Further Developments
• 6. Applications of Admissibility
• References
• Index.

Author/Creator:

Barreira, Luís, 1968- , author

Contributors:

Dragičević, Davor , author

Valls, Claudia, 1973- , author

Languages:

English

Language Notes:

Item content: English

Main Work:

Admissibility and Hyperbolicity [by Barreira, L.]

Other Related Resources:

Print version: Admissibility and Hyperbolicity [by Barreira, L.] (Cham : Springer, 2018 — ISBN 3319901095; ISBN 9783319901091; OCLC Number 1028942231)

Related Series:

SpringerBriefs in mathematics

Subjects:

Mathematics

Difference equations

Functional equations

Dynamics

Ergodic theory

Differential equations

General Notes:

Description based on: Online resource; title from PDF title page (EBSCO, viewed May 9, 2018).

Physical Description:

1 online resource (ix, 145 pages).

Digital Characteristics:

text file

Call Numbers:

QA313 .B377 2018eb

ISBNs:

9783319901107 (electronic bk.)
3319901109 (electronic bk.)
9783319901091 [Invalid]
3319901095 [Invalid]

Other Standard Numbers:

Digital Object Identifier: 10.1007/978-3-319-90110-7

OCLC Numbers:

1034551609