论文标题
双曲线组和半群的特征值差距
Eigenvalue gaps for hyperbolic groups and semigroups
论文作者
论文摘要
鉴于在有限类型的子迁移上局部恒定的线性旋转，我们表明，对于所有不变测量，I-The和（I+1）-th Lyapunov指数之间存在均匀的间隙，这意味着存在索引i的主导拆分。与此类组的Anosov表示有关，我们为来自单词双曲线群的Sofic子缩影建立了类似的结果。我们讨论了有限生成的半群的情况，并在这种情况下提出了Anosov表示的概念。
Given a locally constant linear cocycle over a subshift of finite type, we show that the existence of a uniform gap between the i-th and (i+1)-th Lyapunov exponents for all invariant measures implies the existence of a dominated splitting of index i. We establish a similar result for sofic subshifts coming from word hyperbolic groups, in relation with Anosov representations of such groups. We discuss the case of finitely generated semigroups, and propose a notion of Anosov representation in this setting.
