Rational maps with generalized Sierpinski gasket Julia sets

被引：17

作者：

Devaney, Robert L.

Rocha, Monica Moreno ^{[1
]}

Siegmund, Stefan

机构：

[1] Univ Toronto, Fields Inst, Toronto, ON M5T 3J1, Canada

[2] Boston Univ, Dept Math, Boston, MA 02215 USA

[3] Goethe Univ Frankfurt, Dept Math, D-60325 Frankfurt, Germany

来源：

TOPOLOGY AND ITS APPLICATIONS | 2007年 / 154卷 / 01期

关键词：

rational maps; Julia sets; Sierpinski gaskets;

D O I：

10.1016/j.topol.2006.03.024

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study a family of rational maps acting on the Riemann sphere with a single preperiodic critical orbit. Using a generalization of the well-known Sierpinski gasket, we provide a complete topological description of their Julia sets. In addition, we present a combinatorial algorithm that allows us to show when two such Julia sets are not topologically equivalent. (c) 2006 Elsevier B.V. All rights reserved.

引用

页码：11 / 27

页数：17

共 8 条

[1] Sierpinski-curve Julia sets and singular perturbations of complex polynomials [J].