论文标题
加权Birkhoff平均值的指数收敛
Exponential convergence of weighted Birkhoff average
论文作者
论文摘要
在本文中，我们考虑了Tori上非理性旋转的加权Birkhoff平均值的多项式和指数收敛速率。结果表明，在有限和无限的尺寸托里可以实现这些尺寸，该尺寸分别对应于准二极管和几乎是周期性的动态系统，在非谐振条件与傅立叶系数的衰减速率之间的一定平衡下。提供了有限和无限尺寸的双狂旋转作为示例。我们首次证明了在准碘情况下和分析性下几乎是周期性的情况下指数收敛和任意多项式收敛的普遍性。
In this paper, we consider the polynomial and exponential convergence rate of weighted Birkhoff averages of irrational rotations on tori. It is shown that these can be achieved for finite and infinite dimensional tori which correspond to the quasiperiodic and almost periodic dynamical systems respectively, under certain balance between the nonresonant condition and the decay rate of the Fourier coefficients. Diophantine rotations with finite and infinite dimensions are provided as examples. For the first time, we prove the universality of exponential convergence and arbitrary polynomial convergence in the quasiperiodic case and almost periodic case under analyticity respectively.
