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

Let $\sigma_{K}: \sum_{K}\rightarrow \sum_{K}$ be a shift map. For aninterval $[p,q]\subset[0,1]$, let $D_{\sigma_{K}}([p,q])$ denote the set ofpairs for which the density spectrum of the $\epsilon$-approach time set equals$[p,q]$ when $\epsilon$ is small and $E_{\sigma_{K}}([p,q])$ the set of pairsfor which the density spectrum of the $\epsilon$-approach time set converges to$[p,q]$ when $\epsilon\rightarrow 0^+$. Then $\dim_{H}D_{\sigma_{K}}([p,q])=\dim_{H} E_{\sigma_{K}}([p,q])=2-q$. Moreover,$\mathscr{H}^{2-q}(E_{\sigma_{K}}([p,q]))=1$ when $q=0$ and$\mathscr{H}^{2-q}(E_{\sigma_{K}}([p,q]))=+\infty$ when $q>0$. Meanwhile,$\mathscr{H}^{2-q}(D_{\sigma_{K}}([p,q]))=+\infty$ when $q=1$ and$\mathscr{H}^{2-q}(D_{\sigma_{K}}([p,q]))=0$ when $q<1$.

Hausdorff measure of sets of distributional chaotic pairs for shift maps