Multiplicity of closed characteristics on $ P $-symmetric compact convex hypersurfaces in $ \mathbb{R}^{2n} $

There is a long standing conjecture that there are at least \begin{document}$ n $\end{document} closed characteristics on any compact convex hypersurface id="M4">\begin{document}$ \Sigma in id="M5">\begin{document}$ \mathbb{R}^{2n} $\end{document}. In this paper, we provide some new estimates and prove id="M6">\begin{document}$ [\frac{3n}{4}] id="M7">\begin{document}$ for positive integer id="M8">\begin{document}$ $\end{document}, where id="M9">\begin{document}$ satisfies id="M10">\begin{document}$ = P\Sigma certain class of symplectic matrix id="M11">\begin{document}$ P These results not considered previous papers.