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arXiv · 2308.11582

Coexistence of measures with simple Lyapunov spectrum for fiber-bunched cocycles

Daniel Mitsutani·Jonathan DeWitt
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Abstract

We prove that if a H\"older continuous fiber-bunched cocycle $\hat{A}$ over an invertible hyperbolic transitive shift $\hat{\Sigma}$ satisfies an appropriate strong irreducibility condition on Grassmannians, then $\hat{\Sigma}$ admits an ergodic measure $\hat{\mu}$ with full support and product structure with simple Lyapunov spectrum if and only if any other ergodic measure with full support and product structure also has simple Lyapunov spectrum.

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Daniel Mitsutani, Jonathan DeWitt. 2023-08-22. Coexistence of measures with simple Lyapunov spectrum for fiber-bunched cocycles. https://arxiv.org/abs/2308.11582

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