Geometrization of Piecewise homeomorphisms of the circle

Jérôme Los (1) , Natalia a Viana Bedoya

1 I2M - Institut de Mathématiques de Marseille

In this work we study the following realization problem: given a piecewise homeomorphism Φ : S 1 → S 1 , which geometrical and dynamical conditions on φ are sufficient to realize it as a Bowen-Series-like map associated to a surface group, seen as a discrete subgroup of Homeo + (S 1)?

Domaines: Systèmes dynamiques [math.DS]; Théorie des groupes [math.GR]

Jérôme Los, Natalia a Viana Bedoya. Geometrization of Piecewise homeomorphisms of the circle. 2019. ⟨hal-02382747⟩