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.

引用

页码：163 / 183

页数：21

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