A criterion for density of the isoperiodic leaves in rank 1 affine invariant suborbifolds

Abstract

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 of its leaves in the rank 1 case. We establish a criterion that ensures the density of the leaves and provide two applications of this criterion. The first one is a classification of the dynamical behavior of the leaves of FM when M is Prym eigenform locus in genus 3 and the second provides the first examples of dense isoperiodic leaves in the stratum H(2, 1, 1).