Non-affine horocycle orbit closures on strata of translation surfaces:   new examples
  We investigate specific examples of locally-defined real vector-fields on strata of translation surfaces. Integrating SL(2,R)-loci of Veech surfaces along these vector-fields yield interesting new examples of horocyle-invariant ergodic measures. These measures are supported on closed immersed manifolds with boundary that approach the boundary of strata in a novel way. 
Lucien Clavier
math.DS math.GT