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

Abstract

In this paper, let $n\geq2$ be an integer, $P=diag(-I_{n-κ},I_κ,-I_{n-κ},I_κ)$ for some integer $κ\in[0, n-1)$, and $Σ\subset {\bf R}^{2n}$ be a partially symmetric compact convex hypersurface, i.e., $x\in Σ$ implies $Px\inΣ$. We prove that if $Σ$ is $(r,R)$-pinched with $\frac{R}{r}<\sqrt{\frac{5}{3}}$, then $Σ$ carries at least two geometrically distinct P-symmetric closed characteristics which possess at least $2n-4κ$ 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