1 citations · 3 across the 9 of their papers we have counts for
9 papers
Nil-Bohr Sets and Sums with Bounded Gaps
Yang Cao, Jianjie Zhao
We study the relation between $\NilBohr{d}$ sets and $\SG_d^*$ sets. We prove that every $\NilBohr{d}$ set is an $\SG_d^*$ set, answering a question of Host and Kra. More generally…
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…
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…
Topologically mildly mixing of higher orders along generalized polynomials
Yang Cao, Jianjie Zhao
This paper is devoted to studying the multiple recurrent property of topologically mildly mixing systems along generalized polynomials. We show that if a minimal system is topologi…
Minimal subsystems of given mean dimension in Bernstein spaces
Jianjie Zhao
In this paper, we study the shift on the space of uniformly bounded continuous functions band-limited in a given compact interval with the standard topology of tempered distributio…
Topological multiple recurrence of weakly mixing minimal systems for generalized polynomials
Ruifeng Zhang, Jianjie Zhao
Let be a weakly mixing minimal system, be integer-valued generalized polynomials and be non-degenerate. Then there exists a resid…
Top-nilpotent enveloping semigroups and pro-nilsystems
Jiahao Qiu, Jianjie Zhao
In this paper, it is shown that for , a minimal system is a -step pro-nilsystem if its enveloping semigroup is a -step top-nilpotent group, answering…
Null systems in the non-minimal case
Jiahao Qiu, Jianjie Zhao
In this paper, it is shown that if a dynamical system is null and distal, then it is equicontinuous. It turns out that a null system with closed proximal relation is mean equiconti…
A note on mean equicontinuity
Jiahao Qiu, Jianjie Zhao
In this note, it is shown that several results concerning mean equicontinuity proved before for minimal systems are actually held for general topological dynamical systems. Particu…