Monochromatic nonuniform hyperbolicity
Dynamical Systems
2025-09-15 v3
Abstract
We construct examples of continuous -cocycles which are not uniformly hyperbolic despite having the same non-zero Lyapunov exponents with respect to all invariant measures. The base dynamics can be any non-trivial subshift of finite type. According to a theorem of DeWitt--Gogolev and Guysinsky, such cocycles cannot be H\"older-continuous. Our construction uses the nonuniformly hyperbolic cocycles discovered by Walters in 1984.
Keywords
Cite
@article{arxiv.2408.03878,
title = {Monochromatic nonuniform hyperbolicity},
author = {Jairo Bochi},
journal= {arXiv preprint arXiv:2408.03878},
year = {2025}
}
Comments
v.3: Revised according to the referee reports. Final version, accepted for publication in Trans. Amer. Math. Soc