6 papers · 1 filter
The equivalence of precompactness, zero maximal pattern entropy and bounded mean complexity for finite partitions
Jian Li, Tao Yu, Xianliang Zhong
In this paper, we investigate several types of low complexity of finite partitions, including precompactness, zero maximal pattern entropy, bounded mean complexity and mean equicon…
Return time sets and product recurrence
Jian Li, Xianjuan Liang, Yini Yang
Let be a countable infinite discrete group. We show that a subset of contains a return time set of some piecewise syndetic recurrent point in a compact Hausdorff sp…
Weak disjointness of hypercyclic operators
Jian Li, Qijing Liao, Yonghang Ruan
We study the weak disjointness of hypercyclic operators to advance the classifications of hypercyclic operators. We establish an analogue of the Weiss-Akin-Glasner Theorem from top…
A note on logarithmic mean equicontinuity
Dominik Kwietniak, Jian Li, Habibeh Pourmand
We study the set of harmonic limits of empirical measures in topological dynamical systems. We obtain a characterization of unique ergodicity based of logarithmic (harmonic) mean c…
Dense uniform Li-Yorke chaos for linear operators on a Banach space
Jian Li, Xinsheng Wang
This paper focuses on the dense uniform Li-Yorke chaos for linear operators on a Banach space. Some sufficient conditions and equivalent conditions are established under which the…
Chaos for endomorphisms of completely metrizable groups and linear operators on Fréchet spaces
Zhen Jiang, Jian Li
Using some techniques from topological dynamics, we give a uniform treatment of Li-Yorke chaos, mean Li-Yorke chaos and distributional chaos for continuous endomorphisms of complet…