Atlantis Studies in Dynamical Systems

Lyapunov Exponents of Linear Cocycles

Continuity via Large Deviations

Authors: Duarte, Pedro, Klein, Silvius

  • Unified approach to proving continuity of Lyapunov exponents for various types of linear cocycles
  • Uniform large deviation type estimates established for iterates of general quasi-periodic and random cocycles
  • A general Avalanche Principle for compositions of linear maps derived using a geometric approach
  • A list of related open problems
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eBook $84.99
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  • ISBN 978-94-6239-124-6
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Hardcover $109.00
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About this book

The aim of this monograph is to present a general method of proving continuity of Lyapunov exponents of linear cocycles. The method uses an inductive procedure based on a general, geometric version of the Avalanche Principle. The main assumption required by this method is the availability of appropriate large deviation type estimates for quantities related to the iterates of the base and fiber dynamics associated with the linear cocycle. We establish such estimates for various models of random and quasi-periodic cocycles. Our method has its origins in a paper of M. Goldstein and W. Schlag. Our present work expands upon their approach in both depth and breadth. We conclude this monograph with a list of related open problems, some of which may be treated using a similar approach.

Reviews

“The effort of the authors to make this text self-contained and to make the exposition very clear and delightful was successful, making this monograph an excellent contribution for both graduate student and anyone interested in the continuity of Lyapunov Exponents.” (Paulo Varandas, Mathematical Reviews, June, 2018)

Table of contents (7 chapters)

  • Introduction

    Duarte, Pedro (et al.)

    Pages 1-21

  • Estimates on Grassmann Manifolds

    Duarte, Pedro (et al.)

    Pages 23-79

  • Abstract Continuity of Lyapunov Exponents

    Duarte, Pedro (et al.)

    Pages 81-111

  • The Oseledets Filtration and Decomposition

    Duarte, Pedro (et al.)

    Pages 113-160

  • Large Deviations for Random Cocycles

    Duarte, Pedro (et al.)

    Pages 161-205

Buy this book

eBook $84.99
price for USA in USD (gross)
  • ISBN 978-94-6239-124-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA in USD
  • ISBN 978-94-6239-123-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Lyapunov Exponents of Linear Cocycles
Book Subtitle
Continuity via Large Deviations
Authors
Series Title
Atlantis Studies in Dynamical Systems
Series Volume
3
Copyright
2016
Publisher
Atlantis Press
Copyright Holder
Atlantis Press and the author(s)
eBook ISBN
978-94-6239-124-6
DOI
10.2991/978-94-6239-124-6
Hardcover ISBN
978-94-6239-123-9
Edition Number
1
Number of Pages
XIII, 263
Number of Illustrations
4 b/w illustrations
Topics