论文标题
Ahlfors的规律性和Smale空间的分形维度
Ahlfors regularity and fractal dimension of Smale spaces
论文作者
论文摘要
我们证明，为了达到拓扑结合，每个Smale空间都承认了定期的Bowen措施。鲍恩（Bowen）的马尔可夫分区的建设意味着，史密尔（Smale）空间是拓扑马尔可夫链的因素。后者配备了Parry的措施，该措施是常规的。通过扩展鲍文的建筑，我们创建了一种工具，可以将帕里量的Ahlfors规律转移到Smale空间的Bowen量度。我们方法的重要部分使用紧凑的度量空间上的近似图的精致概念。此外，我们获得了有关Hausdorff的新估计，盒子计数和Assouad尺寸的大量蓝色空间。
We prove that, up to topological conjugacy, every Smale space admits an Ahlfors regular Bowen measure. Bowen's construction of Markov partitions implies that Smale spaces are factors of topological Markov chains. The latter are equipped with Parry's measure which is Ahlfors regular. By extending Bowen's construction we create a tool for transferring the Ahlfors regularity of the Parry measure down to the Bowen measure of the Smale space. An essential part of our method uses a refined notion of approximation graphs over compact metric spaces. Moreover, we obtain new estimates for the Hausdorff, box-counting and Assouad dimensions of a large class of Smale spaces.
