Quadratic-Like Dynamics of Cubic Polynomials

被引：10

作者：

Blokh, Alexander ^{[1
]}

Oversteegen, Lex ^{[1
]}

Ptacek, Ross ^{[1
]}

Timorin, Vladlen ^{[2
,3
]}

机构：

[1] Univ Alabama Birmingham, Dept Math, Birmingham, AL 35294 USA

[2] Natl Res Univ Higher Sch Econ, Fac Math, Vavilova St 7, Moscow 112312, Russia

[3] Independent Univ Moscow, Bolshoy Vlasyevskiy Pereulok 11, Moscow 119002, Russia

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2016年 / 341卷 / 03期

基金：

俄罗斯科学基金会;

关键词：

RATIONAL MAPS;

D O I：

10.1007/s00220-015-2559-6

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

A small perturbation of a quadratic polynomial f with a non-repelling fixed point gives a polynomial g with an attracting fixed point and a Jordan curve Julia set, on which g acts like angle doubling. However, there are cubic polynomials with a non-repelling fixed point, for which no perturbation results into a polynomial with Jordan curve Julia set. Motivated by the study of the closure of the Cubic Principal Hyperbolic Domain, we describe such polynomials in terms of their quadratic-like restrictions.

引用

页码：733 / 749

页数：17

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