Parametrization for a class of Rauzy Fractals | Zendy

Jéfferson Bastos | Zendy; T. Rodrigues de Souza | Zendy

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Parametrization for a class of Rauzy Fractals

Author(s) -

Jéfferson Bastos,

T. Rodrigues de Souza

Publication year - 2019

Publication title -

osaka journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.35

H-Index - 33

ISSN - 0030-6126

DOI - 10.18910/71138

Subject(s) - mathematics , parametrization (atmospheric modeling) , class (philosophy) , fractal , boundary (topology) , integer (computer science) , automaton , polynomial , pure mathematics , combinatorics , discrete mathematics , topology (electrical circuits) , mathematical analysis , computer science , theoretical computer science , physics , artificial intelligence , quantum mechanics , programming language , radiative transfer

In this paper, we study a class of Rauzy fractals Ra given by the polynomial x − ax + x− 1 where a ≥ 2 is an integer. In particular, we give explicitly an automaton that generates the boundary of Ra and using an unusual numeration system we prove that Ra is homeomorphic to a topological disk.

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