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arXiv · 2009.14511

Parameter spaces of locally constant cocycles

Argyrios Christodoulou
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Abstract

This article concerns the locus of all locally constant $\mathrm{SL}(2,\mathbb{R})$-valued cocycles that are uniformly hyperbolic, called the hyperbolic locus. Using the theory of semigroups of M\"obius transformations we introduce a new locus in $\mathrm{SL}(2,\mathbb{R})^N$ which allows us to study the complement of the hyperbolic locus. Our results answer a question of Avila, Bochi and Yoccoz, and Jacques and Short, while motivating a new line of investigation on the subject.

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Argyrios Christodoulou. 2020-09-30. Parameter spaces of locally constant cocycles. https://doi.org/10.1093/imrn%2Frnab116

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