$\R^{2n}$中对称紧凸超曲面闭特征的稳定性
Stability of closed characteristics on symmetric compact convex hypersurfaces in $\R^{2n}$
摘要：
设$Σ\subset\R^{2n}$是关于原点对称的紧致凸超曲面。我们证明了如果$\Sg$携带100多个几何上不同的封闭特征，那么至少它们中的$n-1$必须是非双曲的;如果$\Sg$恰好携带$n$几何上不同的封闭特征，那么它们中的至少两个必须是椭圆的。
英文摘要：
In this article, let $Σ\subset\R^{2n}$ be a compact convex hypersurface which is symmetric with respect to the origin. We prove that if $\Sg$ carries finitely many geometrically distinct closed characteristics, then at least $n-1$ of them must be non-hyperbolic; if $\Sg$ carries exactly $n$ geometrically distinct closed characteristics, then at least two of them must be elliptic.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
