论文标题
局部恒定共生的参数空间
Parameter spaces of locally constant cocycles
论文作者
论文摘要
本文涉及所有局部常数$ \ mathrm {sl}（2，\ mathbb {r}）$的基因座 - 均匀的双曲线，称为双曲线基因座。使用Möbius变换的半群的理论，我们在$ \ mathrm {sl}（2，\ mathbb {r}）^n $中介绍了一个新的基因座，这使我们能够研究双曲线基因座的补充。我们的结果回答了Avila，Bochi和Yoccoz以及Jacques和简短的问题，同时激发了对该主题的新调查。
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.
