# American Institute of Mathematical Sciences

June  2006, 16(2): 411-433. doi: 10.3934/dcds.2006.16.411

## Unique ergodicity for non-uniquely ergodic horocycle flows

 1 Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556-4618, United States 2 Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, United States

Received  April 2005 Revised  August 2005 Published  July 2006

We consider the horocycle flow associated to a $\Z^d$-cover of a compact hyperbolic surface. Such flows have no finite invariant measures, and infinitely many infinite ergodic invariant Radon measures. We prove that, up to normalization, only one of these infinite measures admits a generalized law of large numbers, and we identify such laws.
Citation: François Ledrappier, Omri Sarig. Unique ergodicity for non-uniquely ergodic horocycle flows. Discrete & Continuous Dynamical Systems - A, 2006, 16 (2) : 411-433. doi: 10.3934/dcds.2006.16.411
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