Iteration inequalities of the Maslov PP-index theory with applications

In this paper, the PP-splitting numbers and PP-mean index for a symplectic path starting from the identity with P∈Sp(2n)P∈Sp(2n) are defined first, and then by using the Maslov (P,ω)(P,ω)-index theory for a symplectic path, various inequalities of the Maslov PP-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 PP-symmetric periodic solution of nonlinear autonomous Hamiltonian systems.