On the julia sets of quadratic rational maps
On the julia sets of quadratic rational maps
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DOI：
10.1080/17476939208814540
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发表时间：
1992-04
影响因子：
0.9
通讯作者：
Yin Yongcheng
中科院分区：
文献类型：
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作者：
Yin Yongcheng
设f：+ C是次数d大于1的有理函数。对于fi E N，第n个二进制数被写为fn。集合N（f）={z：fn在z的某个邻域正规）称为稳定集。集合J（f）= 3-N（f）称为Julia集。我们还记得J（f）是一个非空的完美集，J（f）= J（f”），n ∈ N，并且J（f）和N（f）是完全不变的。有许多成分，每一个成分都被称为稳定区域。稳定区域U是周期性的，如果fn（U）= U，对于某个整数n> 0。U最终是周期的，如果对于某些整数n> 0和m 2 0，fm +"（U）= fm（U）。D. Sullivan（[9]，[lo]）证明了每个稳定区域都是最终周期的，并将周期稳定区域分为五种类型：吸引盆、超吸引盆、抛物盆、Siege 1盘和赫尔曼环.本文考虑了二次有理映射的复解析动力系统，完整地描述了Julia集的连通性。任何二次有理函数都是PSL（2 C）共轭于以下形式之一：
Let f:+ C be a rational function with degree d greater than one. For fi E N the nth iterate off is written f n. The set N (f)={z: fn is normal in some neighbourhood of z) is called the stable set. The set J (f)= 3-N (f) is called Julia set. We recall that J (f) is a nonempty perfect set, that J (f)= J (f"), n E N, and that J (f) and N (f) are completely invariant.The stable set N (f) consists of coiiniab! y many cnmponents, each one of which is called a stable region. The stable region U is periodic if fn (U)= U for some integer n> 0. U is eventually periodic if f m+"(U)= f m (U) for some integers n> 0 and m 2 0. D. Sullivan ([9],[lo]) has proved that every stable region is eventually periodic, and that periodic stable regions can be classified into five types-attractive basin, superattractive basin, parabolic basin, Siege1 disk and Herman ring. In this note, we consider the complex analytic dynamical system of quadratic rational maps, and describe completely the connectedness of Julia sets. Any quadratic rational function is PSL (2 C) conjugate to one of forms: