The Boundedness Locus and Baby Mandelbrot Sets for Some Generalized McMullen Maps-Reference-Cited by-同舟云学术

The Boundedness Locus and Baby Mandelbrot Sets for Some Generalized McMullen Maps

Published:2023-07 Issue:09 Volume:33 Page:
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

Boyd Suzanne¹^ORCID,Mitchell Alexander J.²

Affiliation:

1. Department of Mathematical Sciences, University of Wisconsin Milwaukee, P. O. Box 413, Milwaukee, Wisconsin 53201, USA

2. Department of Physical Sciences and Mathematics, Wayne State College, 1111 Main Street, Wayne, Nebraska 68787, USA

Abstract

In this paper, we study rational functions of the form [Formula: see text] with [Formula: see text] fixed and at least [Formula: see text], and hold either [Formula: see text] or [Formula: see text] fixed while the other varies. We locate some homeomorphic copies of the Mandelbrot set in the [Formula: see text]-parameter plane for certain ranges of [Formula: see text], as well as in the [Formula: see text]-plane for some [Formula: see text]-ranges. We use techniques first introduced by Douady and Hubbard [1985] that were applied for the subfamily [Formula: see text] by Devaney [2006]. These techniques involve polynomial-like maps of degree two.

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127423501079

Reference10 articles.

1. A GENERALIZED VERSION OF THE MCMULLEN DOMAIN

2. GEOMETRIC LIMITS OF MANDELBROT AND JULIA SETS UNDER DEGREE GROWTH

3. Baby Mandelbrot sets adorned with halos in families of rational maps

4. Julia sets converging to the unit disk

5. Singular perturbations of complex polynomials