Resonance identity for symmetric closed characteristics on symmetric convex Hamiltonian energy hypersurfaces and its applications

In this paper, we establish a new resonance identity for symmetric closed characteristics on symmetric compact convex hypersurface Σ   in R2nR2n when there exist only finitely many geometrically distinct symmetric closed characteristics. As its applications, some interesting results about the stability and multiplicity of symmetric closed characteristics are obtained, and also we prove that if Σ   is C∞C∞-generic, it carries infinitely many symmetric closed characteristics.