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

Abstract

In this paper, let Σ ⊂ ℝ2n be a symmetric compact convex hypersurface which is (r, R)-pinched with \(\frac{R} {r} < \sqrt {\frac{5} {3}} \) . Then Σ carries at least two elliptic symmetric closed characteristics; moreover, Σ carries at least \(E\left[ {\tfrac{{n - 1}} {2}} \right] + E\left[ {\tfrac{{n - 1}} {3}} \right] \) non-hyperbolic symmetric closed characteristics.