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/

Zendy Plus

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

Zendy Tools

Zendy Open

Let $M=S^{2n+1}/ \Gamma$, $\Gamma$ is a finite group which acts freely andisometrically on the $(2n+1)$-sphere and therefore $M$ is diffeomorphic to acompact space form. In this paper, we first investigate Katok's famous exampleabout irreversible Finsler metrics on the spheres to study the topologicalstructure of the contractible component of the free loop space on the compactspace form $M$, then we apply the result to establish the resonance identityfor homologically visible contractible minimal closed geodesics on everyFinsler compact space form $(M, F)$ when there exist only finitely manydistinct contractible minimal closed geodesics on $(M, F)$. As itsapplications, using this identity and the enhanced common index jump theoremfor symplectic paths proved by Duan, Long and Wang in \cite{DLW2}, we show thatthere exist at least $2n+2$ distinct closed geodesics on every compact spaceform $S^{2n+1}/ \Gamma$ with a bumpy irreversible Finsler metric $F$ under somenatural curvature condition, which is the optimal lower bound due to Katok'sexample.

The optimal lower bound estimation of the number of closed geodesics on Finsler compact space form $S^{2n+1}/ \Gamma$