论文标题
限制对海森伯格·尼尔曼福德（Heisenberg Nilmanifolds）更高排名的定理
Limit theorems for higher rank actions on Heisenberg nilmanifolds
论文作者
论文摘要
本文的主要结果是建立有限的添加剂措施，以实现高级阿贝尔对海森伯格·尼尔曼诺夫（Heisenberg Nilmanifolds）的行动。在动作发电机的全措施中，我们在$（2G+1）$ -Dimensional Heisenberg歧管上构建\ emph {bufetov函数}。我们证明，Bufetov功能的渐近函数描述了高级行动的千古积分的偏差，以提供足够平滑的函数。作为推论，具有方差1的归一化千古积分的分布沿着某些子序列收敛到实际线上的非分级紧凑型措施。
The main result of this paper is a construction of finitely additive measures for higher rank abelian actions on Heisenberg nilmanifolds. Under a full measure set of Diophantine conditions for the generators of the action, we construct \emph{Bufetov functionals} on rectangles on $(2g+1)$-dimensional Heisenberg manifolds. We prove that deviation of the ergodic integral of higher rank actions is described by the asymptotic of Bufetov functionals for a sufficiently smooth function. As a corollary, the distribution of normalized ergodic integrals which have variance 1, converges along certain subsequences to a non-degenerate compactly supported measure on the real line.
