Closed characteristics on partially symmetric compact convex hypersurfaces in R^(2n)

In this paper, we study the multiplicity of closed characteristics on partially symmetric convex compact hypersurfaces in R^(2n). The main ingredient of the proof is a new (P,(omega))-index function and its iteration theory for symplectic matrix paths and some symplectic orthogonal matrix P. This theory yields estimates on this multiplicity via index estimates for a new type of iterations of any symplectic matrix path (gamma):[0,(tau)](right arrow)Sp(2n) defined by (gamma)(t+(tau))=P(gamma)(t)P(gamma) (tau) for any t>=0.