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A divergent Teichmüller geodesic with uniquely ergodic. (English) Zbl 1122.37027

Summary: We construct an example of a quadratic differential whose vertical foliation is uniquely ergodic and such that the Teichmüller geodesic determined by the quadratic differential diverges in the moduli space of Riemann surfaces.

MSC:

37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
37A25 Ergodicity, mixing, rates of mixing
30F60 Teichmüller theory for Riemann surfaces
30F30 Differentials on Riemann surfaces
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References:

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