Hamilton系统非线性问题的一种新方法

A NEW METHOD FOR NONLINEAR PROBLEMS OF HAMILTON SYSTEMS

对可积分的Hamilton系统,加上足够小的扰动,系统的不变环面所代表的规则运动在一定范围内都是可延拓的。但混沌轨道并不能直接通过可积极限的扰动来研究。与可积的极限处想对应的极限是反可积极限,在反可积极限处,系统处于完全混沌状态。在该极限处所有的混沌轨道都存在并且对足够小的扰动可延拓。

For the integrable Hamilton systems, the Invariant tori can be continuation in a certain range if the perturbation of the coupled systems is small enough. But the chaos orbits can not be studied with this perturbation from the integrable limit. The anti-integrable limit is opposite to the integrable limit. At this limit the system is complete chaos and all the chaos orbits can be continuation with small enough perturbation.