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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We study two notions of expansiveness for continuous semiflows: expansivenessin the sense of Alves, Carvalho and Siqueira (2017), and an adaptation ofpositive expansiveness in the sense of Artigue (2014). We prove that if $X$ isa metric space and $\phi$ is an expansive semiflow on $X$ according to thefirst definition, then the semiflow $\phi$ is trivial and the space $X$ isuniformly discrete. In particular, if $X$ is compact then it is finite. Withrespect to the second definition, we prove that if $X$ is a compact metricspace and $\phi$ is a positive expansive semiflow on it, then $X$ is a union ofat most finitely many closed orbits, unbranched tails and isolatedsingularities.

On two notions of expansiveness for continuous semiflows