CONSTRUCTING ATTRACTING CYCLES FOR HALLEY AND SCHRODER MAPS OF POLYNOMIALS

被引：2
|
作者：
Collins, Jared T. [1 ]
机构：
[1] Freed Hardeman Univ, Dept Math & Comp Sci, Henderson, TN 38340 USA
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2017年 / 37卷 / 10期
关键词：
Complex dynamics; extraneous attractors; Halley's method; Schroder's method; polynomials;
D O I：
10.3934/dcds.2017237
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We show that for any set of n distinct points in the complex plane, there exists a polynomial p of degree at most n+1 so that the corresponding Halley and Schroder map for p has the given points as a super-attracting cycle. This improves the result in [1], which shows how to find such a polynomial of degree 3n. Moreover we show that in general one cannot improve upon degree n+1.
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页码：5455 / 5465
页数：11
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