8 papers · 1 filter
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…
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…
Quantitative uniform exponential acceleration of averages along decaying waves
Zhicheng Tong, Yong Li
In this study, utilizing a specific exponential weighting function, we investigate the uniform exponential convergence of weighted Birkhoff averages along decaying waves and delve…