Premium
Stochastic Stability of Lyapunov Exponents and Oseledets Splittings for Semi‐invertible Matrix Cocycles
Author(s) -
Froyland Gary,
GonzálezTokman Cecilia,
Quas Anthony
Publication year - 2015
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21569
Subject(s) - invertible matrix , mathematics , lyapunov exponent , linear subspace , pure mathematics , stability (learning theory) , matrix (chemical analysis) , lyapunov equation , random matrix , eigenvalues and eigenvectors , physics , materials science , quantum mechanics , nonlinear system , machine learning , computer science , composite material
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.