均匀流的不变分布
Invariant Distributions for homogeneous flows
摘要：
我们证明了有限体积齐次流形上的每一个齐次流都有可数个独立的不变分布，除非它与环面上的线性流共轭。我们还证明了同样的结论适用于齐次空间的任何不与环面平移共轭的仿射变换。作为证明的一部分，我们有任何光滑的部分双曲流在任何紧流形有可数许多不同的极小集，因此可数许多不同的遍历概率测度。因此，卡托克和格林菲尔德-瓦拉赫猜想在上述所有情况下都成立。
英文摘要：
We prove that every homogeneous flow on a finite-volume homogeneous manifold has countably many independent invariant distributions unless it is conjugate to a linear flow on a torus. We also prove that the same conclusion holds for every affine transformation of a homogenous space which is not conjugate to a toral translation. As a part of the proof, we have that any smooth partially hyperbolic flow on any compact manifold has countably many distinct minimal sets, hence countably many distinct ergodic probability measures. As a consequence, the Katok and Greenfield-Wallach conjectures hold in all of the above cases.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
