Abstract
The global validity of the symplectic integration method or mapping approach is discussed in this paper. The results show that in the regions of phase space where symplectic integration schemes and the Hamiltonian system possess the same topology, they are effective; but in the regions where the schemes possess some other fixed points than those of the Hamiltonian system, their topologies are different from that of the actual system, thus the symplectic integration method or mapping approach is not effective globally.
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