Characterizing nonuniform hyperbolicity by Mather-type admissibility
Dynamical Systems
2024-09-24 v1
Abstract
We consider linear cocycles acting on Banach spaces which satisfy the assumptions of the multiplicative ergodic theorem. A cocycle is nonuniformly hyperbolic if all Lyapunov exponents are non-zero, which is equivalent to the existence of a tempered exponential dichotomy. We provide an equivalent characterization of nonuniform hyperbolicity in terms of a Mather-type admissibility of a pair of weighted function spaces. As an application we give a short proof of the robustness of tempered exponential dichotomies under small linear perturbation.
Cite
@article{arxiv.2409.14809,
title = {Characterizing nonuniform hyperbolicity by Mather-type admissibility},
author = {Robin Chemnitz and Davor Davor Dragičević},
journal= {arXiv preprint arXiv:2409.14809},
year = {2024}
}