Lyapunov Exponents Of Linear Cocycles

Download or read book Lyapunov Exponents of Linear Cocycles written by Pedro Duarte and published by Springer. This book was released on 2016-03-21 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.