一个哈密顿系统向前Euler格式的同宿轨的不存在性

Non-Existence of Homoclinic Orbits of Forward Euler Scheme in Some Hamiltionian System

针对一个哈密顿系统研究向前Euler格式是否存在同宿轨 .首先证明向前Euler格式的稳定流形在连续系统的同宿轨的内部 ,然后证明此格式的不稳定流形在连续系统的同宿轨的外部 ,从而此格式的稳定流形和不稳定流形不相交 。

In order to study whether forward Euler scheme has homoclinic orbits in some Hamiltonian system, we first proved that the stable manifold of forward Euler scheme is surrounded by the homoclinic orbit of continuous sytem,and then proved that the unstable manifold of the scheme is out of the same homoclinic orbit, thus the stable minifold and the unstable manifold don't intersect each other, hence forward Euler scheme has no homoclinic orbits.