Ergodic properties of the horocycle flow and classification of Fuchsian groups. (English) Zbl 0988.37038

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.


37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
30F35 Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization)
30F30 Differentials on Riemann surfaces
37C30 Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc.
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