Matt Bainbridge, John Smillie, Barak Weiss
Published 2016-03-02Version 1
We study dynamics of the horocycle flow on strata of translation surfaces, introduce new invariants for ergodic measures, and analyze the interaction of the horocycle flow and real Rel surgeries. We use this analysis to complete and extend results of Calta and Wortman classifying horocycle-invariant measures in the eigenform loci. We classify the orbit-closures and prove that every orbit is equidistributed in its orbit-closure. We also prove equidistribution statements regarding limits of sequences of measures, some of which have applications to counting problems.
On Cross Sections to the Geodesic and Horocycle Flows on Quotients of $\operatorname{SL}(2, \mathbb{R})$ by Hecke Triangle Groups $G_q$
Invariants and reversibility in polynomial systems of ODEs
Extreme events for horocycle flows
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