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

Abstract.

Let $\Sigma$ be a compact $C^2$ hypersurface in $\mathbb{R}^{2n}$ bounding a convex set with non-empty interior. In this paper it is proved that there always exist at least n geometrically distinct closed characteristics on $\Sigma$ if $\Sigma$ is symmetric with respect to the origin.