Parameter spaces of locally constant cocycles

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 Möbius 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.

21 pages, 10 figures

Cited by in corpus (1)

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