On polynomials sharing preimages of compact sets, and related questions

被引：13
|
作者：
Pakovich, Fedor [1 ]
机构：
[1] Ben Gurion Univ Negev, Dept Math, IL-84105 Beer Sheva, Israel
来源：
GEOMETRIC AND FUNCTIONAL ANALYSIS | 2008年 / 18卷 / 01期
基金：
以色列科学基金会;
关键词：
Julia sets; commuting polynomials; Ritt's theorems;
D O I：
10.1007/s00039-007-0638-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we give a solution of the following problem: under what conditions on infinite compact sets K-1, K-2 subset of C and polynomials f(1), f(2) do the preimages f(1)(-1){K1} and f(2)(-1){K2} coincide. Besides, we investigate some related questions. In particular, we show that polynomials sharing an invariant compact set distinct from a point have equal Julia sets.
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页码：163 / 183
页数：21
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