Tilings of the plane, Thurston semi-norm and decidability

Jean-René Chazottes (1) , Jean-Marc Gambaudo (2) , François Gautero (3)

1 CPHT - Centre de Physique Théorique [Palaiseau]
2 INLN - Institut Non Linéaire de Nice Sophia-Antipolis
3 JAD - Laboratoire Jean Alexandre Dieudonné

We give a geometric interpretation of the undecidability of the tiling problem in the plane. We show that this problem boils down to prove the existence of zeros of a nonnegative convex function defined on a finite dimensional simplex and related to the Thurston semi-norm.

Mots clés: Wang tilings; branched surfaces; translation surfaces.; translation surfaces

Domaines: Systèmes dynamiques [math.DS]

Jean-René Chazottes, Jean-Marc Gambaudo, François Gautero. Tilings of the plane, Thurston semi-norm and decidability. 2012. ⟨hal-00769022v1⟩