Self-similar tiling systems, topological factors and stretching factors

Maria Isabel Cortez (1) , Fabien Durand (2)

1 DMCC - Departamento de Matemática y Ciencia de la Computación [Santiago de Chile]
2 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée

In this paper we prove that if two self-similar tiling systems, with respective stretching factors $\lambda_1$ and $\lambda_2$, have a common factor which is a non periodic tiling system, then $\lambda_1$ and $\lambda_2$ are multiplicatively dependent.

Mots clés: dynamical systems; cobham; self-similar; tiling

Domaines: Systèmes dynamiques [math.DS]

Maria Isabel Cortez, Fabien Durand. Self-similar tiling systems, topological factors and stretching factors. Discrete and Computational Geometry, 2008, 40 (4), pp.622-640. ⟨hal-00201237⟩