Parametrization for a class of Rauzy fractals

zbMATH Open1435.28009arXiv1409.1168MaRDI QIDQ2631634

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Publication date: 15 May 2019

Published in: (Search for Journal in Brave)

Abstract: In this paper, we study a class of Rauzy fractals ${mathcalR}_a$ given by the polynomial $x^3-a{x}^2+x-1$ where $ageq2$ is an integer. In particular we give explicitly an automaton that generates the boundary of ${mathcalR}_a$ and using an exotic numeration system we prove that ${mathcalR}_a$ is homeomorphic to a topological disk.

Full work available at URL: https://arxiv.org/abs/1409.1168

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