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

Abstract

Let $Σ$ be a compact $C^2$ hypersurface in $\R^{2n}$ 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 $Σ$ if $Σ$ is symmetric with respect to the origin.