5 citations · 7 across the 9 of their papers we have counts for
9 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…
Weighted multiple ergodic averages via analytic observables over : Is exponential pointwise convergence universal?
Zhicheng Tong, Yong Li
By employing an accelerated weighting method, we establish arbitrary polynomial and exponential pointwise convergence for multiple ergodic averages under general balancing conditio…
Full-dimensional KAM torus with frequency-preserving in infinite-dimensional Hamiltonian systems
Zhicheng Tong, Yong Li
In this paper, we present two infinite-dimensional KAM theorems with frequency-preserving for a nonresonant frequency of Diophantine type or even weaker. To be more precise, under…
A generic approach via relative singularity and controllability: Frequency-preserving with arbitrarily weak regularity in parameterized Hamiltonian systems
Zhicheng Tong, Yong Li
In this paper, we introduce a novel and generic approach to prove the persistence of frequency-preserving invariant tori in parameterized Hamiltonian systems, addressing irregular…