# Geometrization of Piecewise homeomorphisms of the circle

Research paper by Jérôme Los, Natalia A. Viana Bedoya

Indexed on: 18 Oct '19Published on: 16 Oct '19Published in: arXiv - Mathematics - Dynamical Systems

#### Abstract

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