4 papers
On balance properties of hypercubic billiard words
Nicolas Bédaride, Valérie Berthé, Antoine Julien
This paper studies balance properties for billiard words. Billiard words generalize Sturmian words by coding trajectories in hypercubic billiards. In the setting of aperiodic order…
Language of a non-minimal billiard trajectory inside a cube
Moussa Barro, Nicolas Bédaride, Julien Cassaigne
We consider a non-minimal billiard trajectory inside the cube. We study the language of the associated orbit when the map is coded with three letters associated to three non-parall…
Freezing phase transition for the Thue-Morse subshift
Nicolas Bédaride, Julien Cassaigne, Pascal Hubert +1
On the full shift on two symbols, we consider the potential defined by where denotes the longest common prefix between the infinite word and an element…
Linear Flows on Translation Prisms
Jayadev S. Athreya, Nicolas Bédaride, W. Patrick Hooper +1
Motivated by the study of billiards in polyhedra, we study linear flows in a family of singular flat -manifolds which we call translation prisms. Using ideas of Furstenberg and…