Lyapunov Exponents of Linear Cocycles: Continuity via Large Deviations (Repost)
Pedro Duarte, &quotLyapunov Exponents of Linear Cocycles: Continuity via Large Deviations&quot
English | 5 Apr. 2016 | ISBN: 9462391238 | 280 Pages | EPUB | 6.45 MB
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 f08r quantities related to the iterates of the base 4nd fiber dynamics associated with the linear cocycle. We establish such estimates f08r various models of r4ndom 4nd quasi-periodic cocycles. Our method has its 08rigins in a paper of M. Goldstein 4nd W. Schlag. Our present w08rk exp4nds upon their approach in both depth 4nd breadth. We conclude this monograph with a list of related open problems, some of which may be treated using a similar approach.