An elementary proof that the Rauzy gasket is fractal
Mark Pollicott, Benedict Sewell
TL;DR
This paper provides a straightforward, elementary proof demonstrating that the Rauzy gasket's Hausdorff dimension is less than two, establishing its fractal nature.
Contribution
It offers the first elementary proof that the Rauzy gasket's Hausdorff dimension is strictly less than two, simplifying previous complex arguments.
Findings
Hausdorff dimension of Rauzy gasket is less than two
Rauzy gasket is a fractal set
Elementary proof method used
Abstract
We present a purely elementary proof that the Rauzy gasket has Hausdorff dimension strictly smaller than two.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Topology and Set Theory · Meromorphic and Entire Functions