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In this article, let $\Sigma\subset\R^{2n}$ be a compact convex hypersurfacewhich is symmetric with respect to the origin. We prove that if $\Sg$ carriesfinitely many geometrically distinct closed characteristics, then at least$n-1$ of them must be non-hyperbolic; if $\Sg$ carries exactly $n$geometrically distinct closed characteristics, then at least two of them mustbe elliptic.

Stability of closed characteristics on symmetric compact convex hypersurfaces in $\R^{2n}$