论文标题
Bedford-McMullen套件的间隙序列和拓扑特性
Gap sequences and Topological properties of Bedford-McMullen sets
论文作者
论文摘要
在本文中，我们研究了Bedford-Mcmullen集的拓扑特性和间隙序列。首先，我们引入拓扑条件，组件分离条件（CSC）和几何条件，即指数速率条件（ERC）。然后，我们证明CSC意味着ERC，并且它们都是获得GAP序列渐近估计的足够条件。我们还探索了Bedford-Mcmullen集的拓扑特性，并证明所有正常的Bedford-McMullen集都带有无限的许多连接组件满足CSC，我们从中获得了Bedford-McMullen集合的间隙序列的渐近估计，而无需任何限制。最后，我们将结果应用于Lipschitz等效性。
In this paper, we study the topological properties and the gap sequences of Bedford-McMullen sets. First, we introduce a topological condition, the component separation condition (CSC), and a geometric condition, the exponential rate condition (ERC). Then we prove that the CSC implies the ERC, and that both of them are sufficient conditions for obtaining the asymptotic estimate of gap sequences. We also explore topological properties of Bedford-McMullen sets and prove that all normal Bedford-McMullen sets with infinitely many connected components satisfy the CSC, from which we obtain the asymptotic estimate of the gap sequences of Bedford-McMullen sets without any restrictions. Finally, we apply our result to Lipschitz equivalence.
