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

Katok conjectured that for every $C^{2}$ diffeomorphism $f$ on a Riemannianmanifold $X$, the set $\{h_{\mu}(f):\mu \text{ is an ergodic measure for }(X,f)\}$ includes $[0, h_{top}(f))$. In this paper we obtained a refinedKatok's conjecture on intermediate metric entropies of ergodic measures withsame level that for a transitive locally maximal hyperbolic set or a transitivetwo-side subshit of finite type, one has $$\mathrm{Int}(\{h_{\mu}(f):\mu\inM_{erg}(f,X) \text{ and }\int\varphi d\mu=a\})=\mathrm{Int}(\{h_{\mu}(f):\mu\inM(f,X) \text{ and }\int\varphi d\mu=a\})$$ for any $a\in \left(\inf_{\mu\inM(f,X)}\int\varphi d\mu, \, \sup_{\mu\in M(f,X)}\int\varphi d\mu\right)$ andany continuous function $\varphi$. In this process, we establish'multi-horseshoe' entropy-dense property and use it to get the goal combinedwith conditional variational principles.

Multi-horseshoe dense property and intermediate entropy property of ergodic measures with same level