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Horospherical dynamics in invariant subvarieties
John Smillie, Peter Smillie, Barak Weiss +1
We consider the horospherical foliation on any invariant subvariety in the moduli space of translation surfaces. This foliation can be described dynamically as the strong unstable…
Horocycle dynamics in rank one invariant subvarieties I: weak measure classification and equidistribution
Jon Chaika, Barak Weiss, Florent Ygouf
Let M be an invariant subvariety in the moduli space of translation surfaces. We contribute to the study of the dynamical properties of the horocycle flow on M. In the context of d…
Isoperiodic dynamics in rank 1 affine invariant orbifolds
Florent Ygouf
Let M be a rank 1 affine invariant orbifold in a stratum of the moduli space of flat surfaces. We show that the leaves of the M-isoperiodic foliation are either all closed or all d…
A criterion for density of the isoperiodic leaves in rank 1 affine invariant suborbifolds
Florent Ygouf
We define on any affine invariant orbifold M a foliation FM that generalises the isoperiodic foliation on strata of the moduli space of translation surfaces and study the dynamics…