Julia sets of subhyperbolic rational functions
Julia sets of subhyperbolic rational functions
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DOI：
10.1080/17476930008815244
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发表时间：
2000-04
期刊：
影响因子：
--
通讯作者：
Shunsuke Morosawa
中科院分区：
文献类型：
--
作者：
Shunsuke Morosawa
本文研究了次双曲有理函数的Julia集。这类函数的Fatou集的单连通吸引分支的边界是闭曲线。我们证明了在一定条件下，它们是Jordan曲线。利用这一结果，我们可以看到牛顿方法的Fatou集（z 3−1 = 0）由Jordan域组成。
In this note, we study the Julia sets of subhyperbolic rational functions. The boundaries of simply connected attracting components of the Fatou sets of such functions are closed curves. We show that, under certain conditions, they are Jordan curves. Making use of this result, we see that the Fatou set of Newton's method for z 3−1 = 0 consists of Jordan domains.