Abstract
Abstract In this paper, let Σ ⊂ R2n be a symmetric compact convex hypersurface. We prove that either there are infinitely many closed characteristics or there exist at least 2[n/2] nonhyperbolic closed characteristics on Σ. Due to the example of weakly non-resonant ellipsoids, this estimate is sharp when n is even. Moreover, we prove that if Σ carries exactly n closed characteristics, then at least n − 2 of them possess irrational mean indices.
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