학술논문
Hausdorff Dimension of Closure of Cycles in d-Maps on the Circle
Document Type
Working Paper
Author
Source
Subject
Language
Abstract
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 $d$.