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arXiv · 2408.13921

Cocycles with Quasi-Conformality I: Stability and abundance

Meysam Nassiri·Hesam Rajabzadeh·Zahra Reshadat
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Abstract

This is the first part of a series of papers devoted to the study of linear cocycles over chaotic systems. In the present paper, we establish the existence of such cocycles that $\mathcal{C}^\alpha$-stably exhibit fiberwise bounded orbits ($\alpha>0$). The proof is based on a new mechanism which yields stable elliptic-type behavior in $\mathrm{GL}(d,\mathbb{R})$ or $\mathrm{SL}(d,\mathbb{R})$ cocycles. Moreover, we show that this phenomenon is $\mathcal{C}^0$-dense among $\mathrm{SL}(d,\mathbb{R})$ cocycles over a shift of finite type without dominated splitting.

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Meysam Nassiri, Hesam Rajabzadeh, Zahra Reshadat. 2024-08-25. Cocycles with Quasi-Conformality I: Stability and abundance. https://doi.org/10.1017/s1474748025101369

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