Nondivergence of horocyclic flows on moduli space

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Cylinder deformations in orbit closures of translation surfaces (2013, methodology): “The key tool is the result of Smillie and Weiss [23] mentioned above.”
Badly approximable vectors on fractals (2005, methodology): “The proof of Proposition 8.3 will appear elsewhere; it is similar to that of [ MW , Thm.”
Quantitative recurrence and large deviations for Teichmüller geodesic flow (2005, methodology): “Other quantitative recurrence results for dynamics on Teichmuller spaces were obtained by Minsky-Weiss [ 20 ] for the case of Teichmuller horocycle flow.”