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

Hui  Liu; Duanzhi Zhang

doi:10.3934/dcds.2016.36.877

Article Contents

2016, Volume 36, Issue 2: 877-893. Doi: 10.3934/dcds.2016.36.877

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

Hui Liu^1, and
Duanzhi Zhang^2,

1.
Key Laboratory of Wu Wen-Tsun Mathematics, Chinese Academy of Sciences, School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui 230026
2.
School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071

Received: February 2014

Published online: August 2015

Abstract / Introduction Related Papers Cited by

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.

Keywords:

Compact convex hypersurfaces,
stable P-symmetric closed characteristics,
P-index iteration,
Hamiltonian system.

Mathematics Subject Classification: Primary: 58E05, 37J45; Secondary: 34C25.

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