The global bifurcation and chaotic behaviours for the crystalline undulator radiation
晶体摆动场辐射系统的全局分叉与混沌行为

Introducing sine-squared potential,the particle motion equation in the crystalline undulator field is reduced to the generalized pendulum equation with a dampping and a force terms in the classical mechanics frame in the dipole approximation.The properties of the phase plane are ananysed for a non-peturbated system by means of Jacobian elliptic function and the elliptic integral,and the solution of the equation and the period of the particle motion for this system are expressed exactly.The global bifurcatio...