9 papers
Optimal rates of uniform convergence for weighted Birkhoff averages via almost all rotations
Zhicheng Tong, Yong Li
In this paper, we investigate weighted Birkhoff averages for toral translations associated with compactly supported weighting functions. By introducing several new analytical techn…
Laskar's frequency map analysis revisited
Zhicheng Tong, Yong Li
In this paper, we establish the exponential convergence of Laskar's pioneering frequency map analysis, strictly improving upon classical polynomial bounds. By utilizing appropriate…
Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity
Zhicheng Tong
Since Krengel's work [Kre78] in 1978, it has been widely known that no effective rate of convergence exists in the ergodic theorem. For toral translations, however, by choosing app…
Sharp regularity of a weighted Sobolev space over and its relation to finitely differentiable KAM theory
Zhicheng Tong, Yong Li
In this paper, we investigate the sharp regularity properties of a special weighted Sobolev space defined on the -dimensional torus, which is of independent interest. As a key…
An infinite-dimensional Kolmogorov theorem and the construction of almost periodic breathers
Zhicheng Tong, Yong Li
In this paper, we present two infinite-dimensional Kolmogorov theorems based on non-resonant frequencies of Bourgain's Diophantine type or even weaker conditions. To be more precis…
Weighted Birkhoff averages: Deterministic and probabilistic perspectives
Zhicheng Tong, Yong Li
In this paper, we survey physically related applications of a class of weighted quasi-Monte Carlo methods from a theoretical, deterministic perspective, and establish quantitative…