Abstract: Simulating the long time dynamic behavior of a nonlinear conservative system of differential equations is an important and challenging problem. One of the main challenges is to design integration methods which possess as good as possible numerical stability and preserve as many as possible of the dynamic properties of the system. In this talk we will explain to what extent the symplectic integration methods can give a stable numerical simulation to the typical dynamics of Hamiltonian systems. The explanation is mainly based on the analysis on preservation and breakdown of dynamic invariants of the systems by symplectic integration.
