Numerical simulation of periodic and quasiperiodic solutions for nonautonomous Hamiltonian systems via the scheme preserving weak invariance Original Research Article

If X(t) is a fundamental matrix of the linear nonautonomous Hamiltonian system dx/dt=JA(t)x(∗) with X(0)TJX(0)=J, then X(t)TJX(t)=J for every t∈R. This symplectic property is called the weak invariance of the system (∗). In this paper we first set up some numerical schemes preserving the weak invariance of the system (∗) for numerical computation of the fundamental matrix X(t) with X(0)TJX(0)=J. Based on the above schemes, we give an algorithm of numerically periodic and numerically quasiperiodic solutions for the nonautonomous Hamiltonian system by using the exponential dichotomy of linear differential systems.