100 citations · 180 across the 18 of their papers we have counts for
20 papers
Sturmian beta-shifts do not have typical periodic optimization
Wen Huang, Oliver Jenkinson, Leiye Xu +1
A shift space is said to have typical periodic optimization (TPO) if the set of Lipschitz functions whose unique maximizing measure is supported on a periodic orbit contains an ope…
An affirmative answer to Owings's sumset question
Wen Huang, Zhengxing Lian, Song Shao +3
We give an affirmative answer to Owings's sumset question: for any -coloring of natural numbers, there is an infinite such that is monochromatic. Mo…
MathCoPilot: An Interactive System for Human-AI Symbiotic Paradigm of Mathematical Research
Junjie Zhang, Jiayu Liu, Wenbin Liu +11
Existing LLM-based theorem provers have achieved impressive results on formal mathematics benchmarks, yet they remain confined to acting as autonomous agents that prove a stated pr…
Typical periodic optimization for dynamical systems: symbolic dynamics
Wen Huang, Oliver Jenkinson, Leiye Xu +1
We develop a new theory of maximizing sets in dynamical systems, for the study of ergodic optimization in systems with weak hyperbolicity but where the Mañé cohomology lemma does n…
Almost Countable Spectrum and Logarithmic Sarnak Conjecture
Wen Huang, Maoru Tan, Leiye Xu
In this paper, we introduce topological dynamical systems with almost countable spectrum. We prove that the Logarithmic Sarnak Conjecture holds for zero-entropy topological dynamic…
Ergodic measures in minimal group actions with finite topological sequence entropy
Chunlin Liu, Xiangtong Wang, Leiye Xu
Let be an infinite discrete countable group and be a minimal -system. In this paper, we prove the supremum of topological sequence entropy of is not less tha…
Directional Pinsker algebra and its applications
Chunlin Liu, Leiye Xu
In this paper, we introduce the directional Pinsker algebra, and construct a skew product to study it. As applications, we show that 1. if a -system with positive dir…
Pinsker -algebra Character and mean Li-Yorke chaos
Chunlin Liu, Rongzhong Xiao, Leiye Xu
Let be an infinite countable discrete amenable group. For any -action on a compact metric space , it is proved that for any sequence consisting of non-em…
Directional Kronecker algebra for -actions
Chunlin Liu, Leiye Xu
In this paper, directional sequence entropy and directional Kronecker algebra for -systems are introduced. The relation between sequence entropy and directional seque…
Directional bounded complexity, mean equicontinuity and discrete spectrum for -actions
Chunlin Liu, Leiye Xu
Given , let be a -system, be a direction vector and . We study $…
Lyapunov optimizing measures and periodic measures for expanding maps
Wen Huang, Leiye Xu, Dawei Yang
We prove that there exists an open and dense subset in the space of expanding self-maps of the circle such that the Lyapunov minimizing measures…
Weak mean equicontinuity for a countable discrete amenable group action
Leiye Xu, Liqi Zheng
The weak mean equicontinuous properties for a countable discrete amenable group acting continuously on a compact metrizable space are studied. It is shown that the weak mea…
Time-restricted sensitivity and entropy
Kairan Liu, Leiye Xu, Ruifeng Zhang
In this paper, we consider measure-theoretical restricted sensitivity and topological restricted sensitivities by restricting the first sensitive time. For a given topological dyna…
Polynomial mean complexity and Logarithmic Sarnak conjecture
Wen Huang, Leiye Xu, Xiangdong Ye
In this paper, we reduce the logarithmic Sarnak conjecture to the -symbolic systems with polynomial mean complexity. By showing that the logarithmic Sarnak conjecture hold…
Weak Horseshoe with bounded-gap-hitting times
Leiye Xu, Junren Zheng
In this paper, we consider weak horseshoe with bounded-gap-hitting times. For a flow , it is shown that if the time one map has weak horseshoe with bounded-gap-hit…
Topological entropy of nonautonomous dynamical systems
Kairan Liu, Yixiao Qiao, Leiye Xu
Let be the space of Borel probability measures on a compact metric space endowed with the weak-topology. In this paper, we prove that if the topological…
Ergodic optimization theory for Axiom A flows
Wen Huang, Zeng Lian, Xiao Ma +2
In this article, we consider the weighted ergodic optimization problem Axiom A attractors of a flow on a compact smooth manifold. The main result obtained in this paper is th…
Ergodic optimization theory for a class of typical maps
Wen Huang, Zeng Lian, Xiao Ma +2
In this article, we consider the weighted ergodic optimization problem of a class of dynamical systems where is a compact metric space and is Lipschitz continuou…
Bounded complexity, mean equicontinuity and discrete spectrum
Wen Huang, Jian Li, Jean-Paul Thouvenot +2
We study dynamical systems which have bounded complexity with respect to three kinds metrics: the Bowen metric , the max-mean metric and the mean metric $\bar{d}_n…
Asymptotic pairs, stable sets and chaos in positive entropy systems
Wen Huang, Leiye Xu, Yingfei Yi
We consider positive entropy -systems for certain countable, discrete, infinite left-orderable amenable groups . By undertaking local analysis, the existence of asymptotic pa…