论文标题
无限群体的共同动力学的共同动力学
Conformal dynamics at infinity for groups with contracting elements
论文作者
论文摘要
本文针对具有合同元素的群体发展了无穷大的保形密度理论。我们首先引入一类收敛边界，包括许多已知的双曲线样边界，在该边界上进行了详细的锥形点和Myrberg点的研究。然后，在收敛边界上建立了共形密度的基本理论，包括沙利文阴影引理和hopf-tsuji-sullivan二分法。这给出了（相对）双曲线组的Gromov和Floyd边界上的共形密度理论，rank-1 cat（0）组的视觉边界以及映射课程组的瑟斯顿边界。除此之外，呼吸功能边界上的保形密度提供了我们一般理论的新重要例子。应用包括鉴定随机步行的泊松边界，分歧组的共生问题，测量CAT（0）组的理论结果和映射类组。
This paper develops a theory of conformal density at infinity for groups with contracting elements. We start by introducing a class of convergence boundary encompassing many known hyperbolic-like boundaries, on which a detailed study of conical points and Myrberg points is carried out. The basic theory of conformal density is then established on the convergence boundary, including the Sullivan shadow lemma and a Hopf--Tsuji--Sullivan dichotomy. This gives a unification of the theory of conformal density on the Gromov and Floyd boundary for (relatively) hyperbolic groups, the visual boundary for rank-1 CAT(0) groups, and Thurston boundary for mapping class groups. Besides that, the conformal density on the horofunction boundary provides a new important example of our general theory. Applications include the identification of Poisson boundary of random walks, the co-growth problem of divergent groups, measure theoretical results for CAT(0) groups and mapping class groups.
