Resonance identity, stability and multiplicity of closed characteristics on compact convex hypersurfaces

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dc.creatorWang, Wei
dc.creatorHu, Xijun
dc.creatorLong, Yiming
dc.date2007-01-22
dc.date2007-01-25
dc.date.accessioned2026-07-07T07:42:48Z
dc.date.available2026-07-07T07:42:48Z
dc.descriptionThere is a long standing conjecture in Hamiltonian analysis which claims that there exist at least $n$ geometrically distinct closed characteristics on every compact convex hypersurface in $\R^{2n}$ with $n\ge 2$. Besides many partial results, this conjecture has been only completely solved for $n=2$. In this paper, we give a confirmed answer to this conjecture for $n=3$. In order to prove this result, we establish first a new resonance identity for closed characteristics on every compact convex hypersurface $\Sg$ in $\R^{2n}$ when the number of geometrically distinct closed characteristics on $\Sg$ is finite. Then using this identity and earlier techniques of the index iteration theory, we prove the mentioned multiplicity result for $\R^6$. If there are exactly two geometrically distinct closed characteristics on a compact convex hypersuface in $\R^4$, we prove that both of them must be irrationally elliptic.
dc.description48 pages, 1 figure, to appear in Duke Math. J
dc.identifierhttps://arxiv.org/abs/math/0701608
dc.identifierhttp://arxiv.org/abs/math/0701608
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/122582
dc.subjectSymplectic Geometry
dc.subject58E05, 37J45, 34C25
dc.titleResonance identity, stability and multiplicity of closed characteristics on compact convex hypersurfaces
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