映照z→e^(az+bz^2)(a,b∈R)的动力系统(Ⅱ)参数平面的分歧结构

Dynamic System of the Mapping z→e^(az+bz^2)(a,b∈R) (Ⅱ)Bifurcation Structure on the Parametric Plane

研究系统ｚ→ｅａｘ＋ｂｘ２（ａ，ｂ Ｒ）在参数（ａ，ｂ）平面上的动力学分歧结构。记Ｄｎｉ＝ {（ａ，ｂ） Ｒ｜ｇａｂ有一个n阶及一个ｉ阶周期稳定域循环（ｎ≤ｉ）}。发现Ｄｎｉ（ｉ＞１）不存在，仅存在Ｄｌｉ，这是一个令我们感到惊异的结果。又进一步发现，Ｄ１ｉ（ｉ＞１）存在于一个小区域Ｄ１*中，在其中Ｄ１ｉ（ｉ＞１）的分歧结构与整个参数平面的分歧结构相类似，十分复杂。

in this paper the dynamic bifurcation structure on the parameteric plane of eaz+bz2 was studied.Denote Dni = 1 (a, b ) R | gab that has one n -- order periodic stable domain cycle and another one i -- orderperiodic stable domain cycle(n i) }. We discover that Dni(n> 1 ) doesn't exist, and only D1i does exist,which is a surprising outcome. It is our further discovery that D1i(i> 1 ) exists in the small domain of D1*,this complicated bifurcation structure is similar to the whole parametric plane's bifurcation structure.