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arXiv · 1504.08060

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

Hui Liu·Duanzhi Zhang
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Abstract

In this paper, let $n\geq2$ be an integer, $P=diag(-I_{n-\kappa},I_\kappa,-I_{n-\kappa},I_\kappa)$ for some integer $\kappa\in[0, n-1)$, and $\Sigma \subset {\bf R}^{2n}$ 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.

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Hui Liu, Duanzhi Zhang. 2015-04-30. Stable P-symmetric closed characteristics on partially symmetric compact convex hypersurfaces. https://arxiv.org/abs/1504.08060

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