论文标题
扩大叶子的最大横向测量
Maximal transverse measures of expanding foliations
论文作者
论文摘要
对于扩展（不稳定）差异的叶状，我们使用自然动力学平均来构建横向测量，我们称之为\ emph {maximal}，描述了给定叶子的迭代如何相交的横截面与叶面的统计数据。对于适当的差异性，我们证明这种平均收敛，甚至呈指数速度，并且极限度量具有有限的千古分解。这些结果是通过将最大横向措施与差异性的最大$ u $ entropy量度相关联获得的。
For an expanding (unstable) foliation of a diffeomorphism, we use a natural dynamical averaging to construct transverse measures, which we call \emph{maximal}, describing the statistics of how the iterates of a given leaf intersect the cross-sections to the foliation. For a suitable class of diffeomorphisms, we prove that this averaging converges, even exponentially fast, and the limit measures have finite ergodic decompositions. These results are obtained through relating the maximal transverse measures to the maximal $u$-entropy measures of the diffeomorphism.
