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

Abstract

Let $\hat{I}\pounds$ 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 $\hat{I}\pounds$ if $\hat{I}\pounds$ is symmetric with respect to the origin.

16 pages