Stable closed characteristics on partially symmetric convex hypersurfaces

AbstractLet n be a positive integer and P=diag(−In−κ,Iκ,−In−κ,Iκ) for some integer κ∈[0,n]. In this paper, we prove that for any convex compact smooth hypersurface Σ in R2n with n⩾2 there always exists at least one closed characteristic on Σ which possesses at least 2n−4κ Floquet multipliers on the unit circle of the complex plane, provided Σ is P-symmetric, i.e., x∈Σ implies Px∈Σ