Hausdorff Dimension of Cantor Series
G. Iommi, B. Skorulski
TL;DR
This paper offers a new approach to solving Kifer's variational formula for the Hausdorff dimension of sets defined by digit frequency in Cantor series expansions, advancing the understanding of fractal dimensions.
Contribution
It presents a novel method to solve Kifer's variational problem, providing a different perspective on the Hausdorff dimension of Cantor series sets.
Findings
Successfully solves Kifer's variational problem
Provides a new approach to Hausdorff dimension calculation
Enhances understanding of digit frequency sets in Cantor series
Abstract
In 1996 Y. Kifer obtained a variational formula for the Hausdorff dimension of the set of points for which the frequencies of the digits in the Cantor series expansion is given. In this note we present a slightly different approach to this problem that allow us to solve the variational problem of Kifer's formula.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Computability, Logic, AI Algorithms · Advanced Topology and Set Theory