强制闭轨道的叶状结构
Foliations forcing closed orbits
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中文总结 AI 辅助
本文刻画了可环3维流形上C²有限深度叶状结构中强制所有横截流存在闭轨道的性质，利用周期端映射构造闭轨道，还通过插入动力插件构造出无闭轨道的C¹流。
中文摘要 AI 辅助
我们研究能迫使所有横截流都存在闭轨道的叶状结构，完全刻画了可环3维流形上C²有限深度叶状结构的这一性质；还表明对许多叶状结构，通过C⁰小修改可破坏该性质。我们利用周期端映射理论构造闭轨道，通过沿吸引保形曲线插入横截叶状结构的动力插件，构造出无闭轨道的C¹流。
英文摘要
We study foliations which force every transverse flow to have a closed orbit. We fully characterize this property among $C^2$ finite depth foliations on atoroidal 3-manifolds. We also show that for many foliations, this property can be broken by a $C^0$-small modification of the foliation. We produce closed orbits using the theory of endperiodic maps, and we construct $C^1$ flows without closed orbits by inserting dynamical plugs transverse to foliations along curves of attracting holonomy.
