16 citations · 35 across the 18 of their papers we have counts for
21 papers
Nonpersistence of full-dimensional tori with polynomial decay in nonlinear Schrödinger equations
Zhicheng Tong, Yong Li
We establish local nonpersistence of full-dimensional invariant tori with polynomially decaying actions for the periodic quintic nonlinear Schrödinger equation \[ iu_t-u_{xx}+T_vu+…
Finiteness of planar central configurations of five bodies for all positive masses: On Smale's sixth problem
Zhe Chen, Zhicheng Tong
We prove that for every choice of five positive masses the planar five-body problem has only finitely many central configurations up to rotation, translation and scaling. This answ…
Package Hallucination Attacks on Coding Agents through Prompt Injection in Rule Files
Yupu Wang, Zhengyuan Jiang, Reachal Wang +1
Modern agentic coding frameworks increasingly rely on community-shared rule files (e.g., AGENTS.md or .cursorrules) to guide autonomous code generation, yet the security risks of t…
Complete characterization of planar linearizability and optimal conjugacy regularity
Zhicheng Tong, Yong Li
We establish a complete characterization of local linearizability for planar diffeomorphisms. For every prescribed hyperbolic real Jordan form, we obtain necessary and suffic…
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…
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…
Towards sharp regularity: Full-dimensional tori in vector fields over
Zhicheng Tong, Yong Li
We consider the linearization of a perturbed vector field over the infinite-dimensional torus , and determine the sharp regularity requirement…
Towards continuity: Universal frequency-preserving KAM persistence and remaining regularity
Zhicheng Tong, Yong Li
Beyond Hölder's type, this paper mainly concerns the persistence and remaining regularity of an individual frequency-preserving KAM torus in a finitely differentiable Hamiltonian s…
Moser's Theorem with Frequency-preserving
Chang Liu, Zhicheng Tong, Yong Li
This paper mainly concerns the KAM persistence of the mapping with intersection property, where…
Universal frequency-preserving KAM persistence via modulus of continuity
Zhicheng Tong, Yong Li
In this paper, we study the persistence and remaining regularity of KAM invariant torus under sufficiently small perturbations of a Hamiltonian function together with its derivativ…
Relation between irrationality and regularity for conjugacy of circle diffeomorphisms to rigid rotations
Zhicheng Tong, Shuyuan Xiao, Yong Li
By introducing the modulus of continuity, we first establish the corresponding cross-ratio distortion estimates under smoothness, and further derive a Denjoy-type inequalit…
KAM theorem on modulus of continuity about parameter
Zhicheng Tong, Jiayin Du, Yong Li
In this paper, we study the Hamiltonian systems $ H\left( {y,x,ξ,\varepsilon } \right) = \left\langle {ω\left( ξ\right),y} \right\rangle + \varepsilon P\left( {y,x,ξ,\varepsilon }…
Exponential convergence of weighted Birkhoff average
Zhicheng Tong, Yong Li
In this paper, we consider the polynomial and exponential convergence rate of weighted Birkhoff averages of irrational rotations on tori. It is shown that these can be achieved for…