Relatively Anosov groups: finiteness, measure of maximal entropy, and reparameterization

Autor:	Kim, Dongryul M., Oh, Hee
Rok vydání:	2024
Předmět:	Mathematics - Dynamical Systems Mathematics - Group Theory Mathematics - Geometric Topology
Druh dokumentu:	Working Paper
Popis:	For a geometrically finite Kleinian group $\Gamma$, the Bowen-Margulis-Sullivan measure is finite and is the unique measure of maximal entropy for the geodesic flow, as shown by Sullivan and Otal-Peign\'e respectively. Moreover, it is strongly mixing by Babillot. We obtain a higher rank analogue of this theorem. Given a relatively Anosov subgroup $\Gamma$ of a semisimple real algebraic group, there is a family of flow spaces parameterized by linear forms tangent to the growth indicator. We construct a reparameterization of each flow space by the geodesic flow on the Groves-Manning space of $\Gamma$ which has an exponentially expanding property along unstable foliations. Using this reparameterization, we prove that the Bowen-Margulis-Sullivan measure of each flow space is finite and is the unique measure of maximal entropy. Moreover, it is strongly mixing. Comment: 46 pages, new abstract
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2404.09745 Zobrazit plný text záznamu View this record from Arxiv