  In this article, let $\Sigma\subset\R^{2n}$ be a compact convex hypersurface
which is symmetric with respect to the origin. We prove that if $\Sg$ carries
finitely 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 must
be elliptic.
