Constructing examples of linear cocycles shows nonuniform hyperbolicity in finite type systems, implying new insights into dynamics.
We construct examples of continuous 2 2 -dimensional linear cocycles which are not uniformly hyperbolic despite having the same nonzero Lyapunov exponents with respect to all invariant measures. The base dynamics can be any nontrivial subshift of finite type. According to a theorem of DeWitt–Gogolev and Guysinsky, such cocycles cannot be Hölder-continuous. Our construction uses the nonuniformly hyperbolic cocycles discovered by Walters in 1984.
No takes yet. Share an insight, caveat, or question.
Bochi et al. (2025) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: