Stochastic Stability of Lyapunov Exponents and Oseledets Splittings for Semi‐invertible Matrix Cocycles. Issue 11 (9th March 2015)

• Record Type: Journal Article
• Authors: Froyland, Gary; González‐Tokman, Cecilia; Quas, Anthony
• Is Part Of: Communications on pure and applied mathematics. Volume 68:Issue 11(2015:Nov.)
• Page Start: 2052
• Page End: 2081
• Publication Date: 2015-03-09
• Subjects: Mathematics -- Periodicals; Mechanics -- Periodicals; Mathématiques -- Périodiques; Mécanique -- Périodiques; 510.5
• DOI: 10.1002/cpa.21569
• Languages: English
• ISSNs: 0010-3640

Abstract

<abstract abstract-type="main"> <title> <x xml:space="preserve">Abstract</x> </title> <p>We establish (i) stability of Lyapunov exponents and (ii) convergence in probability of Oseledets spaces for semi‐invertible matrix cocycles subjected to small random perturbations. The first part extends results of Ledrappier and Young to the semi‐invertible setting. The second part relies on the study of evolution of subspaces in the Grassmannian; the analysis developed here is based on higher‐dimensional Möbius transformations and is likely to be of wider interest. © 2015 Wiley Periodicals, Inc.</p> </abstract>