论文标题
密集的真实的Rel Flow Orbits和绝对时期叶
Dense real Rel flow orbits and absolute period leaves
论文作者
论文摘要
我们显示了在每个群体1形层的每个连接组件的区域上的真实流动的密集轨道的存在，至少具有至少2个不同的零。为此，我们建立了$ {\ rm sl}（2，\ mathbb {r}）$ - 轨道闭合的通用密度标准，基于查找闭合包含horocycle的真实REL流的轨道。可以使用具有周期性水平叶片的全体形态1形式的显式结构来验证该标准。我们的结构还提供了绝对时期叶面的致密叶子和这些基因座的许多亚品质的明确例子。
We show the existence of a dense orbit for real Rel flows on the area-1 locus of every connected component of every stratum of holomorphic 1-forms with at least 2 distinct zeros. For this purpose, we establish a general density criterion for ${\rm SL}(2,\mathbb{R})$-orbit closures, based on finding an orbit of a real Rel flow whose closure contains a horocycle. This criterion can be verified using explicit constructions of holomorphic 1-forms with a periodic horizontal foliation. Our constructions also provide explicit examples of dense leaves of the absolute period foliation and many subfoliations of these loci.
