Stability of symmetric closed characteristics on symmetric compact convex hypersurfaces in ℝ2n under a pinching condition

In this paper, let Σ ⊂ ℝ2n be a symmetric compact convex hypersurface which is (r, R)-pinched with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\frac{R} {r} < \sqrt {\frac{5} {3}} $\end{document} . Then Σ carries at least two elliptic symmetric closed characteristics; moreover, Σ carries at least \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$E\left[ {\tfrac{{n - 1}} {2}} \right] + E\left[ {\tfrac{{n - 1}} {3}} \right] $\end{document} non-hyperbolic symmetric closed characteristics.