Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Recurrence, pointwise almost periodicity and orbit closure relation for
  flows and foliations   In this paper, we obtain a characterizations of the recurrence of a
continuous vector field $w$ of a closed connected surface $M$ as follows. The
following are equivalent: 1) $w$ is pointwise recurrent. 2)$w$ is pointwise
almost periodic. 3) $w$ is minimal or pointwise periodic. Moreover, if $w$ is
regular, then the following are equivalent: 1) $w$ is pointwise recurrent.
2)$w$ is minimal or the orbit space $M/w$ is either $[0,1]$, or $S^1$. 3) $R$
is closed (where $R := \{(x,y) \in M \times M \mid y \in \bar{O(x)} \}$ is the
orbit closure relation). On the other hand, we show that the following are
equivalent for a codimension one foliation $\mathcal{F}$ on a compact manifold:
1) $\mathcal{F}$ is pointwise almost periodic. 2) $\mathcal{F}$ is minimal or
compact. 3) $\mathcal{F}$ is $R$-closed. Also we show that if a foliated space
on a compact metrizable space is either minimal or is both compact and without
infinite holonomy, then it is $R$-closed.

17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
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The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
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The categories of this paper are: eess
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg