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.

16 pages

Cited by in corpus (2)

• On the number of P-invariant closed characteristics on partially symmetric compact convex hypersurfaces in ${\mathbf{R}}^{2n}$
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