Ergodic Properties of the Horocycle Flow and Classification of Fuchsian Groups

@inproceedings{Kaimanovich1999ErgodicPO,
  title={Ergodic Properties of the Horocycle Flow and Classification of Fuchsian Groups},
  author={Vadim A. Kaimanovich},
  year={1999}
}
The paper is devoted to a study of the basic ergodic properties (ergodicity and conservativity) of the horocycle ow on surfaces of constant negative curvature with respect to the Liouville invariant measure. We give several criteria for ergodicity and conservativity and connect them with the classiication of the associated Fuchsian groups. Special attention is given to covering surfaces. In particular, we show that normal subgroups of divergent type Fuchsian groups provide natural examples for… CONTINUE READING