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

中文翻译：

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一级仿射不变轨道中等周期叶密度的准则

我们在任何仿射不变轨道上定义$\mathcal{米}$叶状${\mathcal{F}}^{\mathcal{米}}$概括了平移面模空间层上的等周期叶状结构，并研究了等级 1 情况下叶的动力学。我们建立了一个确保叶子密度的标准，并提供了该标准的两个应用。第一个是叶子的动态行为的分类${\mathcal{F}}^{\mathcal{米}}$什么时候$\mathcal{米}$是属 2 或属 3 中 Prym 本征形轨迹的连通分量，第二个提供了层中密集等周期叶的第一个例子$\mathcal{H}(\mathrm{2个},1,1)$.