Institute for Mathematical Sciences
Y. Minsky and B. Weiss
Nondivergence of Horocyclic Flows on Moduli Space.
Abstract: The earthquake flow and the Teichm\"uller horocycle flow are flows on bundles over the Riemann moduli space of a
surface, and are similar in many respects to unipotent
flows on homogeneous spaces of Lie groups. In analogy
with results of Margulis, Dani and others in the
homogeneous space setting, we prove strong nondivergence
results for these flows. This extends previous work of
Veech. As corollaries we obtain that every closed invariant
set for the earthquake (resp. Teichm\"uller horocycle)
flow contains a minimal set, and that almost every quadratic
differential on a Teichm\"uller horocycle orbit has a
uniquely ergodic vertical foliation.
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