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

Abstract

In this article, let $\Sigma \subset {\mathbb{R}}^{2n}$ 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

References in corpus (2)

• Index iteration theory for symplectic paths with applications to nonlinear Hamiltonian systems
• Stability of closed characteristics on symmetric compact convex hypersurfaces in ${\mathbb{R}}^{2n}$