Duke Mathematical Journal
- Duke Math. J.
- Volume 139, Number 3 (2007), 411-462.
Resonance identity, stability, and multiplicity of closed characteristics on compact convex hypersurfaces
There is a long-standing conjecture in Hamiltonian analysis which claims that there exist at least geometrically distinct closed characteristics on every compact convex hypersurface in with . Besides many partial results, this conjecture has been completely solved only for . In this article, we give a confirmed answer to this conjecture for . In order to prove this result, we establish first a new resonance identity for closed characteristics on every compact convex hypersurface in when the number of geometrically distinct closed characteristics on is finite. Then, using this identity and earlier techniques of the index iteration theory, we prove the mentioned multiplicity result for . If there are exactly two geometrically distinct closed characteristics on a compact convex hypersuface in , we prove that both of them must be irrationally elliptic
Duke Math. J., Volume 139, Number 3 (2007), 411-462.
First available in Project Euclid: 24 August 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)
Secondary: 37J45: Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods 34C25: Periodic solutions
Wang, Wei; Hu, Xijun; Long, Yiming. Resonance identity, stability, and multiplicity of closed characteristics on compact convex hypersurfaces. Duke Math. J. 139 (2007), no. 3, 411--462. doi:10.1215/S0012-7094-07-13931-0. https://projecteuclid.org/euclid.dmj/1187916266