论文标题
非紧凑型组和鲍恩方程的免费半群动作的拓扑压力
Topological pressure of free semigroup actions for non-compact sets and Bowen's equation
论文作者
论文摘要
Climenhaga显示了Bowen方程对紧凑型公制空间的任意子集的适用性。本文的主要目的是概括Climenhaga的主要结果，以免费进行非紧凑型组合的半群动作。我们通过使用Caratheodory-pesin结构介绍了自由半群动作的拓扑压力以及自由半群动作的下限和上限拓扑压力的概念。给出了这些概念的某些特性，其次是三个主要结果。 One is to characterize the Hausdorff dimension of arbitrary subset in term of the topological pressure by Bowen equation, whose points have the positive lower Lyapunov exponents and satisfy a tempered contraction condition, the other is the estimation of topological pressure of a free semigroup action on arbitrary subset of X and the third is the relationship between the upper capacity topological pressure of a skew-product transformation and the upper capacity topological pressure of a free semigroup action with respect to任意子集。
Climenhaga showed the applicability of Bowen equation to arbitrary subset of a compact metric space. The main purpose of this paper is to generalize the main result of Climenhaga to free semigroup actions for non-compact sets. We introduce the notions of the topological pressure and lower and upper capacity topological pressure of a free semigroup action for non-compact sets by using the Caratheodory- Pesin structure. Some properties of these notions are given, followed by three main results. One is to characterize the Hausdorff dimension of arbitrary subset in term of the topological pressure by Bowen equation, whose points have the positive lower Lyapunov exponents and satisfy a tempered contraction condition, the other is the estimation of topological pressure of a free semigroup action on arbitrary subset of X and the third is the relationship between the upper capacity topological pressure of a skew-product transformation and the upper capacity topological pressure of a free semigroup action with respect to arbitrary subset.
