A criterion for density of the isoperiodic leaves in rank one affine invariant orbifolds

Pub Date : 2022-12-28 DOI:10.1112/topo.12279

Florent Ygouf

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引用次数: 1

Abstract

We define on any affine invariant orbifold $M$ a foliation $F^{M}$ 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 $F^{M}$ when $M$ 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 $H (2, 1, 1)$ .

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一阶仿射不变轨道中等周期叶密度的一个判据

我们在任何仿射不变的orbifold M$\mathcal｛M｝$上定义了一个叶理FM$\math cal｛F｝^｛\mathcal｝｝$，它推广了平移面的模空间的层上的等周期叶理，并且对1级叶片的动态特性进行了研究。我们建立了一个确保叶片密度的标准，并提供了该标准的两个应用。第一个是当M$\mathcal｛M｝$是亏格2或3中Prym本征型轨迹的连通分量并且第二个例子提供了层H（2，1，1）$\mathcal｛H｝（2，1,1）$中稠密等周期叶的第一个例子。

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