A group from a map and orbit equivalence

Jérôme Los (1, 2) , Natalia Viana Bedoya (3)

1 I2M - Institut de Mathématiques de Marseille
2 AMU - Aix Marseille Université
3 UFSCar - Universidade Federal de São Carlos [São Carlos]

In two papers published in 1979, R. Bowen and R. Bowen and C. Series introduced a dynamical system from a Fuchsian group, acting on the hyperbolic plane H 2. The dynamics is a map on S 1 which is, in particular, an expanding piecewise homeomorphism of the circle. In this paper we consider a reverse question: which dynamical conditions for an expanding piecewise homeomorphism of S 1 are sufficient for the map to be a "Bowen-Series-type" map (see below) for some group G and which groups can occur? We give a partial answer to these questions.

Domaines: Mathématiques [math]

Jérôme Los, Natalia Viana Bedoya. A group from a map and orbit equivalence. 2022. ⟨hal-03834648v2⟩