On the symmetric intersection of Rauzy fractals associated with the k-bonacci substitution

Hamdi Ammar (1) , Julien Cassaigne (2) , Tarek Sellami (1)

1 Université de Sfax - University of Sfax
2 I2M - Institut de Mathématiques de Marseille

In this article, we study the intersection of Rauzy fractals associated with the k-bonacci substitution and its reversed substitution. Applying balanced pair algorithm to these two substitutions, we characterise all minimal balanced pairs, and we obtain a general formula for the associated intersection substitution. This substitution is defined over k(k+1)/2 letters.

Mots clés: substitutions; k-bonacci; balanced pairs algorithm; fractal sets

Domaines: Systèmes dynamiques [math.DS]

Hamdi Ammar, Julien Cassaigne, Tarek Sellami. On the symmetric intersection of Rauzy fractals associated with the k-bonacci substitution. Quaestiones Mathematicae, 2021, 44 (2), pp.199-216. ⟨10.2989/16073606.2019.1680455⟩. ⟨hal-02375081⟩