Stable P-symmetric closed characteristics on partially symmetric compact convex hypersurfaces

Abstract

In this paper, let $n\ge 2$ be an integer, $P=diag(-I_{n-\kappa },I_{\kappa },-I_{n-\kappa },I_{\kappa })$ for some integer $\kappa \in [0,n-1)$, and $\Sigma \subset {\mathbf{R}}^{2n}$ be a partially symmetric compact convex hypersurface, i.e., $x\in \Sigma$ implies $Px\in \Sigma$. We prove that if $\Sigma$ is $(r,R)$-pinched with $\frac{R}{r}<\sqrt{\frac{5}{3}}$, then $\Sigma$ carries at least two geometrically distinct P-symmetric closed characteristics which possess at least $2n-4\kappa$ Floquet multipliers on the unit circle of the complex plane.

21 pages. To appear in DCDS-A. arXiv admin note: text overlap with arXiv:0812.0049, arXiv:0909.3564, arXiv:0812.0041 by other authors