论文标题
无穷大的压力和负弯曲的强正复发
Pressure at infinity and strong positive recurrence in negative curvature
论文作者
论文摘要
在非伴随弯曲的歧管的地球流量的背景下，我们通过周期性轨道的生长，Poincaré系列的关键指数以及不变措施的熵（压力）提出了三种不同的熵和无限压力定义。我们表明这些概念是一致的。由于这些熵和无穷大的压力，我们在这种几何环境下彻底研究了强烈复发的概念。当其无穷大的压力严格小于全拓扑压力时，其潜力强烈反复出现。我们特别表明，如果潜力是强烈的反复反复出现的，那么它将接受有限的吉布斯度量。我们还提供了简单的标准，可以建立如此强大的积极反复发作的潜力和许多例子。
In the context of geodesic flows of noncompact negatively curved manifolds, we propose three different definitions of entropy and pressure at infinity, through growth of periodic orbits, critical exponents of Poincaré series, and entropy (pressure) of invariant measures. We show that these notions coincide. Thanks to these entropy and pressure at infinity, we investigate thoroughly the notion of strong positive recurrence in this geometric context. A potential is said strongly positively recurrent when its pressure at infinity is strictly smaller than the full topological pressure. We show in particular that if a potential is strongly positively recurrent, then it admits a finite Gibbs measure. We also provide easy criteria allowing to build such strong positively recurrent potentials and many examples.
