ON A PROOF OF THE TREE CONJECTURE FOR TRIANGLE TILING BILLIARDS

Sur une preuve de la conjecture d'arbre pour les billards dans les pavages triangulaires

Olga Paris-Romaskevich (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

Tiling billiards model a movement of light in heterogeneous medium consisting of homogeneous cells in which the coefficient of refraction between two cells is equal to −1. The dynamics of such billiards depends strongly on the form of an underlying tiling. In this work we consider periodic tilings by triangles (and cyclic quadrilaterals), and define natural foliations associated to tiling billiards in these tilings. By studying these foliations we manage to prove the Tree Conjecture for triangle tiling billiards that was stated in the work by Baird-Smith, Davis, Fromm and Iyer, as well as its generalization that we call Density property.

Domaines: Systèmes dynamiques [math.DS]; Combinatoire [math.CO]

Olga Paris-Romaskevich. ON A PROOF OF THE TREE CONJECTURE FOR TRIANGLE TILING BILLIARDS. 2019. ⟨hal-02169195v1⟩