English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we obtain a characterizations of the recurrence of acontinuous vector field $w$ of a closed connected surface $M$ as follows. Thefollowing are equivalent: 1) $w$ is pointwise recurrent. 2)$w$ is pointwisealmost periodic. 3) $w$ is minimal or pointwise periodic. Moreover, if $w$ isregular, 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 theorbit closure relation). On the other hand, we show that the following areequivalent for a codimension one foliation $\mathcal{F}$ on a compact manifold:1) $\mathcal{F}$ is pointwise almost periodic. 2) $\mathcal{F}$ is minimal orcompact. 3) $\mathcal{F}$ is $R$-closed. Also we show that if a foliated spaceon a compact metrizable space is either minimal or is both compact and withoutinfinite holonomy, then it is $R$-closed.

Recurrence, pointwise almost periodicity and orbit closure relation for flows and foliations