Irrationally elliptic closed characteristics on symmetric compact convex hypersurfaces in R^8

Abstract

Let $\Sigma$ be a $C^3$ compact symmetric convex hypersurface in $\mathbb{R}^{8}$. We prove that when $\Sigma$ carries exactly four geometrically distinct closed characteristics, then there are at least two irrationally elliptic closed characteristics on $\Sigma$.