Ergodic properties of the horocycle flow and classification of Fuchsian groups (Q1570898)

This paper deals with the study of the ergodicity and conservativity of the horocycle flow on surfaces of constant negative curvature with respect to the Liouville invariant measure. The author presents several criteria for ergodicity and conservativity. He shows that normal subgroups of divergent-type Fuchsian groups provide natural examples for the strictness of a number of inclusions in the classifications of Fuchsian groups.