Geometrization of Piecewise homeomorphisms of the circle

Jérôme Los; Natalia A. Viana Bedoya

Geometrization of Piecewise homeomorphisms of the circle

Dynamical Systems 2022-11-16 v4 Group Theory

Authors: Jérôme Los , Natalia A. Viana Bedoya

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 ${\rm Homeo}^+ (S^1)$ ?

Keywords

piecewise homeomorphisms circle Bowen-Series map surface group geometrization realization problem discrete subgroup

Cite

@article{arxiv.1910.07609,
  title  = {Geometrization of Piecewise homeomorphisms of the circle},
  author = {Jérôme Los and Natalia A. Viana Bedoya},
  journal= {arXiv preprint arXiv:1910.07609},
  year   = {2022}
}

Comments

This work has been merged into arXiv:2211.00637 under the title 'A group from a map and orbit equivalence'

Geometrization of Piecewise homeomorphisms of the circle

Abstract

Keywords

Cite

Comments

Related papers