My talk is a kind of review of problems and recent results regarding smooth curvesin the moduli space of translation surfaces and Teichmüller positive
semi-orbits starting from such curves. I plan to present some abstract results about the
recurrence or equidistribution of Teichmüller positive semi-orbits starting from almost every element
of the curve. The main part of the talk are applications that motivate abstract results. Two
main applications relate to billiards on nibbled ellipses and impact Hamiltonian systems. |