椭圆Kepler方程求解中的非线性现象

NONLINEAR PHENOMENA IN SOLVING KEPLERS EQUATION IN THE CASE OF ELLIPTIC ORBITS

讨论用具立方收敛的改进的牛顿法解椭圆运动中Ｋｅｐｌｅｒ方程时出现的各种非线性现象，包括多重周期点、奇异吸因子和多周期混沌带．当初值固定而参数变化时出现了典型的倍周期解和混沌带分岔现象．此外，发现了参数平面上的不收敛区有复杂的自相似分形结构．

This paper discusses various nonlinear phenomena in solving Keplers equation in the elliptic case by an improved newtonian method with cubic convergence, which include multiperiodic points and chaotic belts, and strange attractors. Typical branches of period doubling occur with the increase of one of the parameters when the initial value is fixed. Especially, we have found that the region of nonconvergence in the plane of parameters has a selfsimilar and fractal structure.