Stability of closed characteristics on compact convex hypersurfaces in $\R^6$

Details Stability of closed characteristics on compact convex hypersurfaces in $\R^6$ Stability of closed characteristics on compact convex hypersurfaces in $\R^6$

2007-01-24

arxiv.org/abs/math/0701673v3

Mathematics

Symplectic Geometry

24 pages, to appear in J. Eur. Math. Soc

Scientific paper

In this paper, let $\Sigma\subset\R^{6}$ be a compact convex hypersurface. We
prove that if $\Sigma$ carries only finitely many geometrically distinct closed
characteristics, then at least two of them must possess irrational mean
indices. Moreover, if $\Sg$ carries exactly three geometrically distinct closed
characteristics, then at least two of them must be elliptic.

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