Lyapunov Exponents of Linear Cocycles: Continuity via Large Deviations

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Springer, Mar 21, 2016 - Mathematics - 263 pages
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.
 

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Contents

1 Introduction
1
2 Estimates on Grassmann Manifolds
23
3 Abstract Continuity of Lyapunov Exponents
81
4 The Oseledets Filtration and Decomposition
113
5 Large Deviations for Random Cocycles
161
6 Large Deviations for QuasiPeriodic Cocycles
207
7 Further Related Problems
247
Index
261
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