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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We consider a group $G$ acting on a local dendrite $X$ (in particular on agraph). We give a full characterization of minimal sets of $G$ by showing thatany minimal set $M$ of $G$ (whenever $X$ is different from a dendrite) iseither a finite orbit, or a Cantor set, or a circle. If $X$ is a graphdifferent from a circle, such a minimal $M$ is a finite orbit. These resultsextend those of the authors for group actions on dendrites. On the other hand,we show that, for any group $G$ acting on a local dendrite $X$ different from acircle, the following properties are equivalent: (1) ($G, X$) is pointwisealmost periodic. (2) The orbit closure relation $R = \{(x, y)\in X\times X:y\in \overline{G(x)}\}$ is closed. (3) Every non-endpoint of $X$ is periodic.In addition, if $G$ is countable and $X$ is a local dendrite, then ($G, X$) ispointwise periodic if and only if the orbit space $X/G$ is Hausdorff.

Minimal sets and orbit space for group actions on local dendrites