发表机构
Baylor University（贝勒大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对高维拟周期环面旋转建立了定量Denjoy-Koksma型估计，得到Hölder连续观测函数的最尖锐Birkhoff平均收敛速度，并将其应用于空间拟周期Hamilton-Jacobi方程的均匀化及不变测度正则性估计。
AI 中文摘要
本文针对高维拟周期环面旋转建立了定量的Denjoy-Koksma型估计。对于丢番图频率向量，我们对具有各类Besov型正则性的观测函数，建立了Birkhoff平均与空间平均之间偏差的定量估计。通过合适的Sobolev嵌入，这些估计给出了据我们所知目前可获得的、针对Hölder连续观测函数的最尖锐收敛速度。作为应用，我们在空间拟周期情形下获得了Hamilton-Jacobi方程大幅改进的定量均匀化结果，以及扰动下不变测度的近最优统计正则性估计。
英文摘要
In this paper, we establish quantitative Denjoy--Koksma type estimates for higher-dimensional quasi-periodic torus rotations. For Diophantine frequency vectors, we establish quantitative estimates on the discrepancy between Birkhoff averages and spatial averages for observables with various Besov-type regularities. The Besov framework is naturally adapted to the small-divisor structure of the problem, allowing a sharp analysis of resonant frequencies and yielding optimal rates throughout the entire parameter range. These estimates yield, to the best of our knowledge, the sharpest currently available convergence rates for Hölder continuous observables. As applications, we obtain substantially improved quantitative homogenization results for Hamilton--Jacobi equations in spatially quasi-periodic settings, as well as nearly optimal statistical regularity estimates for invariant measures under perturbations.
Comments45 pages. The main theorem covers the full range of parameters
