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

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

2008-11-29

arxiv.org/abs/0812.0041v1

Mathematics

Symplectic Geometry

18 pages

Scientific paper

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.

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