Dimension rigidity for cookie-cutter Cantor sets

2018/09/19 by Ingebretson, Daniel
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1809.07414

Abstract

We show that two cookie-cutter Cantor sets with the same symbolic coding are differentiably equivalent if and only if their Hausdorff dimensions are equal.

Related

• Classifying Cantor Sets by their Fractal Dimensions
• Exact Hausdorff and Packing measure of certain Cantor sets, not\n necessarily self-similar or homogeneous
• Exact Hausdorff Measure of Certain Non-Self-Similar Cantor Sets
• Squeezing functions and Cantor Sets
• Stable intersections of regular conformal Cantor sets with large Hausdorff dimensions