What is a rauzy fractal?

Document Type : Translation Paper

Authors

University of Yazd

Abstract

This paper is a translation of the the following paper into Persian:
[P. Arnoux and E. Harriss, What is a Rauzy fractal?, Notice of the AMS, 61 no. 7 (2014) 768-770.]

According to an ancient tradition, it is possible to associate symbolic and infinite words with dynamical systems. Conversely, for infinite words generated by algebraic or combinatorial methods, it is possible to provide geometric representations, which can be a family of self-similar sets with fractal boundaries. As an example, in this article, we study fractals called Rauzy fractals.

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References

[1] M. Barge and J. Kwapisz, Geometric theory of unimodular Pisot substitutions, Amer. J. Math., 128 no. 5 (2006) 1219–1282.
[2] N. Pytheas Fogg, edited by V. Berthé, S. erenczi, C. Mauduit and A. Siegel, Substitutions in Dynamics, Arithmetics and Combinatorics, Lecture Notes in Mathematics, 1794, Springer-Verlag, Berlin, 2002.
[3] G. Rauzy, Nombres algébriques et substitutions, Bull. Soc. Math. France, 110 no. 2 (1982) 147–178.
[4] M. Senechal, Quasicrystals and Geometry, Cambridge University Press, 1995.
[5] P. Arnoux and E. Harriss, What is a Rauzy fractal?, Notice of the AMS, 61 no. 7 (2014) 768-770.
Mathematics and Society
Volume 1, Issue 3 - Serial Number 3
September 2016
Pages 39-43

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