广义高阶零流的有效等分布
Effective equidistribution for generalized higher step nilflows
摘要：
本文的主要结果是证明了一般高阶幂零流形上的幂零流的遍历平均的界。在流的环面投影频率的丢番图条件下，我们证明了几乎所有的轨道都以多项式速度成为等分布的。我们用一般幂零李代数的阶数和结构决定的衰减速度来分析幂零指数。主要结果来自于控制不可约表示中尺度算子的技巧和一般流形上闭返回轨道的测度估计。
英文摘要：
The main results of this paper are to prove bounds for ergodic averages for nilflows on general higher step nilmanifolds. Under Diophantine condition on the frequency of a toral projection of the flow, we prove that almost all orbits become equidistributed at the polynomial speed. We analyze the exponent with the speed of decay which is determined by the number of steps and structure of general nilpotent Lie algebras. The main result follows from the technique over controlling scaling operators in irreducible representations and measure estimation on close return orbit on general nilmanifolds.
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