Stability of closed characteristics on compact convex hypersurfaces in R^{2n}

Abstract

Let $\Sigma \subset {\mathbb{R}}^{2n}$ with $n\ge 2$ be any $C^2$ compact convex hypersurface and only has finitely geometrically distinct closed characteristics. Based on Y.Long and C.Zhu 's index jump methods \cite{LoZ1}, we prove that there are at least two geometrically distinct elliptic closed characteristics, and moreover, there exist at least ${\varrho }_n(\Sigma )$ (${\varrho }_n(\Sigma )\ge [\frac{n}{2}]+1$) geometrically distinct closed characteristics such that for any two elements among them, the ratio of their mean indices is irrational number.

22pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:0812.0041, arXiv:math/0109116 by other authors

References in corpus (1)

• Stability of closed characteristics on compact convex hypersurfaces in ${\mathbb{R}}^6$