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arXiv · 2502.17145

Slicing the Torus and the thermodynamics of self-similar measures with overlaps

Peej Ingarfield
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Abstract

Orthogonal projections of the uniform measure on the Sierpinski triangle form a family of self similar measures with overlaps. The main result of this work is to make a connection between the dimension theory of these measures and the thermodynamic formalism of the doubling map restricted to rational slices of the torus. Of note is how we establish a correspondence between the varying translational parameter and varying rational slices. This gives a new direction from which to understand the dimension theory of projections of self similar measures.

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Peej Ingarfield. 2025-02-24. Slicing the Torus and the thermodynamics of self-similar measures with overlaps. https://arxiv.org/abs/2502.17145

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