Multiple P-cyclic symmetric closed characteristics on compact convex P-cyclic symmetric hypersurfaces in {ℝ}^{2n}

Abstract

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 \sum \subset {ℝ}^{2n} with n≥2 which is P-cyclic symmetric, i.e., x\mathrm{\in }\sum implies P_x\mathrm{\in }\sum ; we prove that if \sumis (r;R)-pinched with ,then there exist at least n geometrically distinct P-cyclic symmetric closed characteristics on \sum for a broad class of matrices P:

Key words： Compact convex hypersurfaces; Hamiltonian system; P-cyclic symmetric closed characteristics; multiplicity

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