We define on any affine invariant orbifold M a foliation F M 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 F M 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).
We classify the non arithmetic rank one affine invariant orbifolds that do not arise from Veech surfaces in H(3, 1) and H odd (2, 2). We also give rigidity results on the isoperiodic leaf of non arithmetic Veech surfaces.
We define on any affine invariant orbifold a foliation that generalizes 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 when is a connected component of a Prym eigenform locus in genus 2 or 3 and the second provides the first examples of dense isoperiodic leaves in the stratum (2, 1, 1).
Let ${\mathcal {M}}$ be a rank 1 affine invariant orbifold in a stratum of the moduli space of flat surfaces. We show that the leaves of the ${\mathcal {M}}$-isoperiodic foliation are either all closed or all dense. In the 2nd case, we establish ergodicity of the foliation with respect to the affine measure on ${\mathcal {M}}$.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.