03225nam 22006135 450 991025406830332120220407231621.094-6239-124-610.2991/978-94-6239-124-6(CKB)3710000000621858(EBL)4454920(SSID)ssj0001654083(PQKBManifestationID)16433927(PQKBTitleCode)TC0001654083(PQKBWorkID)14982492(PQKB)10382215(DE-He213)978-94-6239-124-6(MiAaPQ)EBC4454920(PPN)192770357(EXLCZ)99371000000062185820160321d2016 u| 0engur|n|---|||||txtccrLyapunov exponents of linear cocycles continuity via large deviations /by Pedro Duarte, Silvius Klein1st ed. 2016.Paris :Atlantis Press :Imprint: Atlantis Press,2016.1 online resource (271 p.)Atlantis Studies in Dynamical Systems ;3Description based upon print version of record.94-6239-123-8 Includes bibliographical references at the end of each chapters and index.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.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.Atlantis Studies in Dynamical Systems ;3DynamicsErgodic theoryMathematical physicsDynamical Systems and Ergodic Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M1204XMathematical Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/M35000Dynamics.Ergodic theory.Mathematical physics.Dynamical Systems and Ergodic Theory.Mathematical Physics.510Duarte Pedroauthttp://id.loc.gov/vocabulary/relators/aut755963Klein Silviusauthttp://id.loc.gov/vocabulary/relators/autBOOK9910254068303321Lyapunov Exponents of Linear Cocycles2044169UNINA