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arXiv · 2605.11848

Cocycles with Quasi-Conformality II: Ergodic measures with positive entropy

Meysam Nassiri·Hesam Rajabzadeh·Zahra Reshadat
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Abstract

As the second part of a series on linear cocycles over chaotic systems, this paper establishes a "multiple covering principle" that robustly yields positive-entropy ergodic measures supported on fiberwise uniformly bounded orbits. Using this mechanism, we prove that any continuous $\mathrm{SL}(d,\mathbb{R})$ cocycle over a positive-entropy subshift of finite type either admits a dominated splitting or can be $\mathcal{C}^0$-approximated by one that \emph{stably} supports such measures. The stability holds in H\"older topology which is optimal. Additionally, for non-isometric cocycles, we show that the topological entropy of these bounded orbits is strictly less than that of the base subshift.

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Meysam Nassiri, Hesam Rajabzadeh, Zahra Reshadat. 2026-05-12. Cocycles with Quasi-Conformality II: Ergodic measures with positive entropy. https://arxiv.org/abs/2605.11848

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