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math.DS2026
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…
math.DS2026
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…
math.DS2026
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…