论文标题
圆圈中循环闭合的Hausdorff尺寸
Hausdorff Dimension of Closure of Cycles in d-Maps on the Circle
论文作者
论文摘要
我们研究了单位圆圈上地图$ x $至$ dx $（mod 1）的动态。我们表征了该地图的不变有限子集，该子集称为循环，并按其程度进行评分。通过查看循环中元素基本d扩展的组合性能，我们证明了Curt McMullen的猜想，即闭合度-M循环的Hausdorff维度等于log $ m $ / log $ $ $ d $。
We study the dynamics of the map $x$ to $dx$ (mod 1) on the unit circle. We characterize the invariant finite subsets of this map which are called cycles and are graded by their degrees. By looking at the combinatorial properties of the base-d expansion of the elements in the cycles, we prove a conjecture of Curt McMullen that the Hausdorff dimension of the closure of degree-m cycles is equal to log $m$ / log $d$.
