TY  - BOOK
AU  - Duarte,Pedro
AU  - Klein,Silvius
ED  - SpringerLink (Online service)
TI  - Lyapunov Exponents of Linear Cocycles: Continuity via Large Deviations 
T2  - Atlantis Studies in Dynamical Systems
SN  - 9789462391246
AV  - QA313 
U1  - 515.39 23
PY  - 2016///
CY  - Paris
PB  - Atlantis Press, Imprint: Atlantis Press
KW  - Differentiable dynamical systems
KW  - Dynamical Systems and Ergodic Theory
KW  - Mathematical Physics
N1  - Introduction -- Estimates on Grassmann Manifolds -- Abstract Continuity of Lyapunov Exponents -- The Oseledets Filtration and Decomposition -- Large Deviations for Random Cocycles -- Large Deviations for Quasi-Periodic Cocycles -- Further Related Problems
N2  - 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
UR  - https://doi.org/10.2991/978-94-6239-124-6
ER  -