Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Transitive points via Furstenberg family   Let $(X,T)$ be a topological dynamical system and $\mathcal{F}$ be a
Furstenberg family (a collection of subsets of $\mathbb{Z}_+$ with hereditary
upward property). A point $x\in X$ is called an $\mathcal{F}$-transitive one if
$\{n\in\mathbb{Z}_+:\, T^n x\in U\}\in\F$ for every nonempty open subset $U$ of
$X$; the system $(X,T)$ is called $\F$-point transitive if there exists some
$\mathcal{F}$-transitive point. In this paper, we aim to classify transitive
systems by $\mathcal{F}$-point transitivity. Among other things, it is shown
that $(X,T)$ is a weakly mixing E-system (resp.\@ weakly mixing M-system,
HY-system) if and only if it is $\{\textrm{D-sets}\}$-point transitive (resp.\@
$\{\textrm{central sets}\}$-point transitive, $\{\textrm{weakly thick
sets}\}$-point transitive).
  It is shown that every weakly mixing system is $\mathcal{F}_{ip}$-point
transitive, while we construct an $\mathcal{F}_{ip}$-point transitive system
which is not weakly mixing. As applications, we show that every transitive
system with dense small periodic sets is disjoint from every totally minimal
system and a system is $\Delta^*(\mathcal{F}_{wt})$-transitive if and only if
it is weakly disjoint from every P-system.

10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph