An upper bound on the dimension of the Rauzy gasket
Mark Pollicott, Benedict Sewell
TL;DR
This paper provides an elementary proof establishing that the Hausdorff dimension of the Rauzy gasket does not exceed 1.7407, refining previous upper bounds and contributing to the understanding of its fractal geometry.
Contribution
The paper introduces a new elementary proof technique to improve the upper bound on the Hausdorff dimension of the Rauzy gasket.
Findings
Hausdorff dimension of Rauzy gasket ≤ 1.7407
Improved upper bound over previous results
Elementary proof method used
Abstract
In this note, we give an elementary proof that the Hausdorff dimension of the Rauzy gasket is at most 1.7407, improving upon results of Avila et al. and Fougeron.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Differential Equations and Dynamical Systems · Advanced Topology and Set Theory