Journal of the European Mathematical Society


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Volume 11, Issue 3, 2009, pp. 575–596
DOI: 10.4171/JEMS/161

Published online: 2009-06-30

Stability of closed characteristics on compact convex hypersurfaces in 6

Wei Wang[1]

(1) Peking University, Beijing, China

Let Σ ⊂ 6 be a compact convex hypersurface. We prove that if Σ carries only finitely many geometrically distinct closed characteristics, then at least two of them must have irrational mean indices. Moreover, if Σ carries exactly three geometrically distinct closed characteristics, then at least two of them must be elliptic.

Keywords: Compact convex hypersurfaces, closed characteristics, Hamiltonian systems, Morse theory, mean index identity, stability

Wang Wei: Stability of closed characteristics on compact convex hypersurfaces in 6. J. Eur. Math. Soc. 11 (2009), 575-596. doi: 10.4171/JEMS/161