Linearly repetitive Delone systems have a finite number of non periodic Delone system factors

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

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

We prove linearly repetitive Delone systems have finitely many Delone system factors up to conjugacy. This result is also applicable to linearly repetitive tiling systems.

Mots clés: Delone sets; tiling systems; factor maps; linearly repetitive; voronoï cell

Domaines: Systèmes dynamiques [math.DS]

Maria Isabel Cortez, Fabien Durand, Samuel Petite. Linearly repetitive Delone systems have a finite number of non periodic Delone system factors. Proceedings of the American Mathematical Society, 2010. ⟨hal-00300649⟩