Stability of closed characteristics on compact hypersurfaces in $\R^{2n}$ under pinching condition

Abstract

In this article, let $Σ\subset\R^{2n}$ be a compact convex hypersurface which is $(r, R)$-pinched with $\frac{R}{r}<\sqrt{3/2}$. Then $\Sg$ carries at least two strictly elliptic closed characteristics; moreover, $\Sg$ carries at least $2[\frac{n+2}{4}]$ non-hyperbolic closed characteristics.

18 pages