Stochastic Stability of Lyapunov Exponents and Oseledets Splittings for Semi‐invertible Matrix Cocycles | Zendy

Froyland Gary | Zendy; GonzálezTokman Cecilia | Zendy; Quas Anthony | Zendy

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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 , stability (learning theory) , pure mathematics , matrix (chemical analysis) , lyapunov equation , random matrix , eigenvalues and eigenvectors , computer science , materials science , physics , quantum mechanics , machine learning , composite material , artificial intelligence , chaotic

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.

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