Iteration inequalities of the Maslov [formula omitted]-index theory with applications

Abstract

In this paper, the P-splitting numbers and P-mean index for a symplectic path starting from the identity with P∈Sp(2n) are defined first, and then by using the Maslov (P,ω)-index theory for a symplectic path, various inequalities of the Maslov P-index theory for iterations of symplectic paths starting from the identity are established. As an application, these results are used to study the minimal period problem of P-symmetric periodic solution of nonlinear autonomous Hamiltonian systems.