时间改变的首行幂零作用的定向测度刚性
Directional measure rigidity for time-changed first row unipotent actions
浏览论文内容
中文总结 AI 辅助
本文研究高秩阿贝尔幂零作用时间改变的定向流，在有限体积齐性流形上证明Ratner型刚性：定量余循环条件迫使流为代数且测度齐性，并给出紧致情形下光滑共轭的充要条件及精确渐近。
中文摘要 AI 辅助
我们研究有限体积齐性流形上的流，这些流作为高秩阿贝尔幂零作用的时间改变的定向限制而出现。我们在此设定中建立了Ratner型刚性结果。对于$\noperatorname{SL}_n(\nmathbb{R})$的有限体积商上的首行作用，我们证明了关于余循环的自然定量假设迫使该流为代数流，且其遍历不变测度为齐性测度。这些结果推广到高维子作用以及一般抽象设定。我们还证明了，在$\noperatorname{SL}_3(\nmathbb{R})$的紧商上，光滑时间改变通过保持叶的微分同胚光滑共轭于线性代数作用，当且仅当定向流的余循环沿一个方向具有有界偏差。我们还获得了紧致根增量的精确渐近行为。我们结果中的主要阈值是精确的。
英文摘要
We study flows on finite volume homogeneous manifolds arising as directional restrictions of time changes of higher rank abelian unipotent actions. We establish Ratner-type rigidity results in this setting. For first row actions on finite volume quotients of $\operatorname{SL}_n(\mathbb{R})$, we show that natural quantitative assumptions on the cocycle force the flow to be algebraic and its ergodic invariant measure to be homogeneous. These results extend to higher dimensional subactions and to a general abstract setting. We also show that, on compact quotients of $\operatorname{SL}_3(\mathbb{R})$, the smooth time change is smoothly conjugate to a linear algebraic action by a leaf preserving diffeomorphism if and only if the cocycle of the directional flow has bounded deviations along one direction. We also obtain precise asymptotics for compact root increments. The principal thresholds in our results are sharp.
发表机构
- Université de Lille（里尔大学）
- National University of Singapore（新加坡国立大学）
机构由 AI 辅助整理，请以论文原文为准。
