On the Hausdorff dimension of invariant measures for multicritical circle maps

TL;DR

This paper provides explicit bounds on the Hausdorff dimension of the unique invariant measure for multicritical circle maps, linking these bounds to the arithmetic properties of the rotation number.

Contribution

It offers new explicit bounds for the Hausdorff dimension of invariant measures in multicritical circle maps based on rotation number properties.

Findings

Bounds depend solely on arithmetic properties of the rotation number

Explicit bounds are provided for the Hausdorff dimension

Results apply to $C^3$ multicritical circle maps without periodic points

Abstract

We give explicit bounds for the Hausdorff dimension of the unique invariant measure of $C^3$ multicritical circle maps without periodic points. These bounds depend only on the arithmetic properties of the rotation number.