THE JACARANDA TREE IS STRONGLY APERIODIC AND HAS ZERO ENTROPY

L'arbre binaire colorié Jacaranda est fortement apériodique et d'entropie nulle.

Alexandre Baraviera (1) , Renaud Leplaideur (2, 3)

1 UFRGS - Departamento de Matemática Pura e Aplicada [Porto Alegre]
2 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique
3 ISEA - Institut de sciences exactes et appliquées

We prove that the Jacaranda tree obtained as a fixed point for a substreetution in previous work of the authors is strongly aperiodic and that the number of patches increases linearly with respect to the size of the patch. As a consequence we get that the tree has zero entropy.

Domaines: Systèmes dynamiques [math.DS]

Alexandre Baraviera, Renaud Leplaideur. THE JACARANDA TREE IS STRONGLY APERIODIC AND HAS ZERO ENTROPY. 2023. ⟨hal-04055327⟩