论文标题
关于麦古德二分法的报告
A report on an ergodic dichotomy
论文作者
论文摘要
我们建立了HölderCocycles，Patterson-Sullivan措施等单词杂种基团的LEDRAPPIER对应关系的（某些方向）。然后，我们在本地字段上研究了$θ$ -Anosov表示的Patterson-Sullivan度量，并证明这些措施是由表示形式的$θ$ - 关键性超出表面进行了参数。我们使用这些Patterson-Sullivan措施来建立有关$θ$ - 限制锥体内部方向的二分法：如果$ u $是这样的一半，则$ u $ u $ conical限制点的子集总数为$ | fe | fe | feq2 $ | $ | fee | fee | fece | fece | fecy | fece | fecy | fece | fecy | fece | fece | fecy | fece | fece | fece | fece | fime | fime |未安排。
We establish (some directions) of a Ledrappier correspondence between Hölder cocycles, Patterson-Sullivan measures, etc for word-hyperbolic groups with metric-Anosov Mineyev flow. We then study Patterson-Sullivan measures for $θ$-Anosov representations over a local field and show that these are parametrized by the $θ$-critical hypersurface of the representation. We use these Patterson-Sullivan measures to establish a dichotomy concerning directions in the interior of the $θ$-limit cone of the representation in question: if $u$ is such a half-line, then the subset of $u$-conical limit points has either total-mass if $|θ|\leq2$ or zero-mass if $|θ|\geq4.$ The case $|θ|=3$ remains unsettled.
