哈密顿系统能量守恒格式的同宿轨的存在性与收敛性

EXISTENCE AND CONVERGENCE OF HOMOCLINIC ORBITS OF ENERGY CONSERVATIVE SCHEME IN HAMILTONIAN SYSTEM

研究在什么条件下 ,用能量守恒格式能够计算出哈密顿系统的同宿轨 .通过连续化的方法给出了能够计算出同宿轨的条件 .并且证明了在连续系统存在同宿轨以及连续系统和相应的离散系统存在能够包括连续系统的同宿轨的二维不变流形 ,并互相以 p 阶逼近的情况下 ,能量守恒格式存在同宿轨且此同宿轨以

Studies the conditions under which the homoclinic orbits can be computed for energy conservative scheme in Hamiltonian system,and the conditions established by means of continuation method for compution of the homoclinic orbits,and proves that the energy conservative scheme has homoclinic orbits approximating to those of the original system with p_th order if the continuous system has a homoclinic orbit and the continuous system and corresponding discrete system have 2_dimensional manifolds (containing a homoclinic orbit of continuous system) which approximate each other with p_the order.