9 papers
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…
Mean Li-Yorke chaos for a sequence of operators on Banach spaces
Jian Li, Xinsheng Wang, Jianjie Zhao
In this paper, we obtain the dichotomy for mean equicontinuity and mean sensitivity for a sequence of bounded linear operators from a Banach space to a normed linear space. The mea…
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…
Density properties of orbits for a hypercyclic operator on a Banach space
Jian Li, Xinsheng Wang, Jianjie Zhao
We study density properties of orbits for a hypercyclic operator on a separable Banach space , and show that exactly one of the following four cases holds: (1) every vector…