For certain Veech surfaces, the paper shows that the Teichmüller geodesic flow pushes twist tori to dense sets, and under an algebraic monodromy condition every weak-* limit is fully supported.
Tremors and horocycle dynamics on the moduli space of translation surfaces
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abstract
We introduce a "tremor" deformation on strata of translation surfaces. Using it, we give new examples of behaviors of horocycle flow orbits in strata of translation surfaces. In the genus two stratum with two singular points, we find orbits which are generic for a measure whose support is strictly contained in the orbit and find orbits which are not generic for any measure. We also describe a horocycle orbit-closure whose Hausdorff dimension is not an integer.
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Veech Surfaces and Expanding Twist Tori on Moduli Spaces of Abelian Differentials
For certain Veech surfaces, the paper shows that the Teichmüller geodesic flow pushes twist tori to dense sets, and under an algebraic monodromy condition every weak-* limit is fully supported.