函数zexp(z+a+πi)的动力学

Dynamics of the function z exp(z+a+πi)

研究函数fa(z)=zexp(z+a+πi)的动力学,证明了下列结果:当a<0时,Fatou集F(fa)是一个完全不变吸引域;存在an>0,使得fan具有2n阶超吸引域,而当a>an时,fa没有2n阶超吸引域;an单调增加趋于无穷大;集合B0={aRJ(fa)=C}是一个无界集.

In this paper , dynamics of the function fa （z） = z exp （z ＋ a ＋ πi） is studied. The following results have been proved. The Fatou set f（fa） is a completely invariant absorbing domain for a 〈 0. There exists an 〉 0 such that fan has super absorbing domains of 2n-order, but fa has no super absorbing domains of 2n-order for a 〉 an. Furthermore, a, is monotone increasing toward infinity. The set B0 = {a∈R｜J（fa） = C} is unbounded.