Multiple P-cyclic symmetric closed characteristics on compact convex P-cyclic symmetric hypersurfaces in R~(2n)

摘要

Let k ≥ 2 be an integer and P be a 2n × 2n symplectic orthogonal matrix satisfying P~k = I_(2n) and ker(P~j - I_(2n)) = 0, 1 ≤ j ＜ k. For any compact convex hypersurface ∑ ⊂ R~(2n) with n ≥ 2 which is P-cyclic symmetric, i.e., x ∈ ∑ implies Px ∈ ∑, we prove that if ∑ is (r, R)-pinched with R/r ＜ ((2k+2)/k)~(1/2) then there exist at least n geometrically distinct P-cyclic symmetric closed characteristics on ∑ for a broad class of matrices P.