关于双曲流形的幂幺标架流的拓扑和可测动力学
On topological and measurable dynamics of unipotent frame flows for hyperbolic manifolds
摘要：
研究无限体积双曲流形标架丛上的幂幺流动力学。只要测地流有一个极大熵的有限测度，并且这个极大熵严格大于极大幂幺流内幂幺流的编码，我们就证明了它们是拓扑传递的，并且自然的不变测度，即所谓的“Burger-Roblin测度“是遍历的.后一个结果推广了Mohammadi和Oh的一个定理。
英文摘要：
We study the dynamics of unipotent flows on frame bundles of hyperbolic manifolds of infinite volume. We prove that they are topologi-cally transitive, and that the natural invariant measure, the so-called " Burger-Roblin measure ", is ergodic, as soon as the geodesic flow admits a finite measure of maximal entropy, and this entropy is strictly greater than the codi-mension of the unipotent flow inside the maximal unipotent flow. The latter result generalises a Theorem of Mohammadi and Oh.
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