Higher <i>P</i>-symmetric Ekeland-Hofer capacities

Abstract

&lt;p style='text-indent:20px;'&gt;This paper is devoted to the construction of analogues of higher Ekeland-Hofer symplectic capacities for &lt;inline-formula&gt;&lt;tex-math id="M2"&gt;\begin{document}$ P $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;-symmetric subsets in the standard symplectic space &lt;inline-formula&gt;&lt;tex-math id="M3"&gt;\begin{document}$ (\mathbb{R}^{2n},\omega_0) $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;, which is motivated by Long and Dong's study about &lt;inline-formula&gt;&lt;tex-math id="M4"&gt;\begin{document}$ P $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;-symmetric closed characteristics on &lt;inline-formula&gt;&lt;tex-math id="M5"&gt;\begin{document}$ P $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;-symmetric convex bodies. We study the relationship between these capacities and other capacities, and give some computation examples. Moreover, we also define higher real symmetric Ekeland-Hofer capacities as a complement of Jin and the second named author's recent study of the real symmetric analogue about the first Ekeland-Hofer capacity.&lt;/p&gt;