Finiteness of gibbs measures on noncompact manifolds with pinched negative curvature
Finiteness of gibbs measures on noncompact manifolds with pinched negative curvature
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DOI：
10.5802/aif.3167
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发表时间：
2016-10
期刊：
影响因子：
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通讯作者：
Barbara Schapira;Vincent Pit
中科院分区：
文献类型：
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作者：
Barbara Schapira;Vincent Pit
我们的特点是有限的吉布斯措施的测地线流负弯曲流形的几个标准，类似于由Sarig提出的符号动力系统在一个无限的字母表。作为应用，我们恢复了几何有限双曲流形上Bowen-Margulis测度有限性的Dal'bo-Otal-Peign{\' e}判据，以及几何无限流形具有有限Bowen-Margulis测度的Peign{\'e}例子.这些标准应该是有用的，在未来找到更多的例子与有限吉布斯措施。
We characterize the finiteness of Gibbs measures for geodesic flows on negatively curved manifolds by several criteria, analogous to those proposed by Sarig for symbolic dynamical systems over an infinite alphabet. As an application, we recover Dal'bo-Otal-Peign{\'e} criterion of finiteness for the Bowen-Margulis measure on geometrically finite hyperbolic manifolds, as well as Peign{\'e}' examples of gemetrically infinite manifolds having a finite Bowen-Margulis measure. These criteria should be useful in the future to find more examples with finite Gibbs measures.