The unique measure of maximal entropy for a compact rank one locally CAT(0) space
The unique measure of maximal entropy for a compact rank one locally CAT(0) space
复制标题
DOI：
10.3934/dcds.2020266
复制
发表时间：
2019-06
期刊：
影响因子：
--
通讯作者：
Russell Ricks
中科院分区：
文献类型：
--
作者：
Russell Ricks
设$X$是一个紧致的、测地完备的局部CAT(0)空间，使得万能覆盖有一个秩一轴。证明了测地线空间上的Bowen-Marguis测度是测地线流的最大熵的唯一度量，它的拓扑熵等于Poincare级数的临界指数。
Let $X$ be a compact, geodesically complete, locally CAT(0) space such that the universal cover admits a rank one axis. We prove the Bowen-Margulis measure on the space of geodesics is the unique measure of maximal entropy for the geodesic flow, which has topological entropy equal to the critical exponent of the Poincare series.