The Weil-Petersson geodesic flow is ergodic

Mathematics – Dynamical Systems

Scientific paper

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53 pages. Errors corrected in earlier version and some expository material removed. To appear in Annals of Math

Scientific paper

We prove that the geodesic flow for the Weil-Petersson metric on the moduli
space of Riemann surfaces is ergodic (in fact Bernoulli) and has finite,
positive metric entropy.

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