The generic points for the horocycle flow on a class of hyperbolic surfaces with infinite genus

Omri Sarig (1) , Barbara Schapira (2)

1 Mathematics department, Penn State University
2 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée

A point is called generic for a flow preserving an infinite ergodic invariant Radon measure, if its orbit satisfies the conclusion of the ratio ergodic theorem for every pair of continuous functions with compact support and non-zero integrals. The generic points for horocycle flows on hyperbolic surfaces of finite genus are understood, but there are no results in infinite genus. We give such a result, by characterizing the generic points for $\Z^d$--covers.

Mots clés: horocycle flow; infinite genus; equidistribution; ratio ergodic theorem; Babillot-Ledrappier measures

Domaines: Systèmes dynamiques [math.DS]

Omri Sarig, Barbara Schapira. The generic points for the horocycle flow on a class of hyperbolic surfaces with infinite genus. International Mathematics Research Notices, 2008, ⟨10.1093/imrn/rnn086⟩. ⟨hal-00263806⟩