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Unique ergodicity for non-uniquely ergodic horocycle flows

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  • 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.
    Mathematics Subject Classification: Primary: 37A17; Secondary: 37A40.


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