Advertisement

Lyapunov Exponents of Linear Cocycles

Continuity via Large Deviations

  • Pedro Duarte
  • Silvius Klein
Book

Part of the Atlantis Studies in Dynamical Systems book series (ASDS, volume 3)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Pedro Duarte, Silvius Klein
    Pages 1-21
  3. Pedro Duarte, Silvius Klein
    Pages 23-79
  4. Pedro Duarte, Silvius Klein
    Pages 81-111
  5. Pedro Duarte, Silvius Klein
    Pages 113-160
  6. Pedro Duarte, Silvius Klein
    Pages 161-205
  7. Pedro Duarte, Silvius Klein
    Pages 207-246
  8. Pedro Duarte, Silvius Klein
    Pages 247-260
  9. Back Matter
    Pages 261-263

About this book

Introduction

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.

Keywords

Bernoulli Cocycles Large Deviations Lyapunov Exponents Quasi-periodic Cocycles Subharmonic Functions

Authors and affiliations

  • Pedro Duarte
    • 1
  • Silvius Klein
    • 2
  1. 1.Universidade de LisboaFaculdade de Ciências daLisboaPortugal
  2. 2.Department of Mathematical SciencesNTNUTrondheimNorway

Bibliographic information