Semigroups of Isometries of the Hyperbolic Plane
Semigroups of Isometries of the Hyperbolic Plane
Motivated by a problem on the dynamics of compositions of plane hyperbolic isometries, we prove several fundamental results on semigroups of isometries, thought of as real M\"obius transformations. We define a semigroup $S$ of M\"obius transformations to be \emph{semidiscrete} if the identity transformation is not an accumulation point of $S$. …