A GENERALIZED VERSION OF THE MCMULLEN DOMAIN-Reference-Cited by-同舟云学术

A GENERALIZED VERSION OF THE MCMULLEN DOMAIN

Published:2008-08 Issue:08 Volume:18 Page:2309-2318
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

BLANCHARD PAUL¹,DEVANEY ROBERT L.¹,GARIJO ANTONIO¹²,RUSSELL ELIZABETH D.¹

Affiliation:

1. Department of Mathematics and Science, Boston University, Boston, MA 02215, USA

2. Dep. d'Eng. Informàtica i Matemàtiques, Universitat Rovira i Virgili, Av. Països Catalans, 26, 43007 Tarragona, Spain

Abstract

We study the family of complex maps given by Fλ(z) = zn + λ/zn + c where n ≥ 3 is an integer, λ is an arbitrarily small complex parameter, and c is chosen to be the center of a hyperbolic component of the corresponding Multibrot set. We focus on the structure of the Julia set for a map of this form generalizing a result of McMullen. We prove that it consists of a countable collection of Cantor sets of closed curves and an uncountable number of point components.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127408021725

Reference13 articles.

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

2. SINGULAR PERTURBATIONS OF QUADRATIC MAPS

3. The escape trichotomy for singularly perturbed rational maps

4. The McMullen domain: Rings around the boundary

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