有限型粗膨胀共形动力学
Finite type coarse expanding conformal dynamics
摘要：
我们继续研究具有膨胀行为的不可逆拓扑动力系统。我们引入了一类{ \em有限型}系统，其特征在于的条件下，直到重新缩放和一致有界的失真，只有100多个迭代。我们证明了具有有界价和网格趋于零的次双曲有理映射和有限细分规则（在Cannon，Floyd，Kenyon和Parry意义下）是有限型的。此外，我们还证明了与自相似、收缩、常返、水平传递群作用（在V. Nekrashevych意义下）相关联的极限动力系统是有限型的。证明必要地利用了双曲群所具有的锥型性质的有限性的类比。
英文摘要：
We continue the study of non-invertible topological dynamical systems with expanding behavior. We introduce the class of {\em finite type} systems which are characterized by the condition that, up to rescaling and uniformly bounded distortion, there are only finitely many iterates. We show that subhyperbolic rational maps and finite subdivision rules (in the sense of Cannon, Floyd, Kenyon, and Parry) with bounded valence and mesh going to zero are of finite type. In addition, we show that the limit dynamical system associated to a selfsimilar, contracting, recurrent, level-transitive group action (in the sense of V. Nekrashevych) is of finite type. The proof makes essential use of an analog of the finiteness of cone types property enjoyed by hyperbolic groups.
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