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

In this paper, we first establish the Bott-type iteration formulas and someabstract precise iteration formulas of the Maslov-type index theory associatedwith a Lagrangian subspace for symplectic paths. As an application, we provethat there exist at least $[\frac{n}{2}]+1$ geometrically distinct brake orbitson every $C^2$ compact convex symmetric hypersurface $\Sigma$ in$\mathbb{R}^{2n}$ satisfying the reversible condition $N\Sigma=\Sigma$,furthermore, if all brake orbits on this hypersurface are nondegenerate, thenthere are at least $n$ geometrically distinct brake orbits on it. As aconsequence, we show that there exist at least $[\frac{n}{2}]+1$ geometricallydistinct brake orbits in every bounded convex symmetric domain in$\mathbb{R}^{n}$, furthermore, if all brake orbits in this domain arenondegenerate, then there are at least $n$ geometrically distinct brake orbitsin it. In the symmetric case, we give a positive answer to the Seifertconjecture of 1948 under a generic condition.

Iteration theory of $L$-index and Multiplicity of brake orbits