Geometrization of Piecewise homeomorphisms of the circle

Abstract

In this work we study the following realization problem: given a piecewise homeomorphism $\Phi :S^1\to S^1$, 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 ${\mathrm{Homeo}}^{+}(S^1)$?

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

Cited by in corpus (1)

• Combining Rational maps and Kleinian groups via orbit equivalence