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

被引：0
|
作者：
Boyd, Suzanne [1 ]
Mitchell, Alexander J. [2 ]
机构：
[1] Univ Wisconsin Milwaukee, Dept Math Sci, POB 413, Milwaukee, WI 53201 USA
[2] Wayne State Coll, Dept Phys Sci & Math, 1111 Main St, Wayne, NE 68787 USA
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2023年 / 33卷 / 09期
关键词：
Complex dynamical system; Mandelbrot set; polynomial-like map; rational map; iteration; JULIA SETS; DYNAMICS; FAMILIES; HALOS;
D O I：
10.1142/S0218127423501079
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study rational functions of the form R-n,R-a,R-c(z) = z(n) + a/z(n) + c, with n fixed and at least 3, and hold either a or c fixed while the other varies. We locate some homeomorphic copies of the Mandelbrot set in the c-parameter plane for certain ranges of a, as well as in the a-plane for some c-ranges.We use techniques first introduced by Douady and Hubbard [1985] that were applied for the subfamily R-n,R-a,R-0 by Devaney [2006]. These techniques involve polynomial-like maps of degree two.
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