@inproceedings{1ea483233d594d4fb8c6043549438191,

title = "Simple Mandelpinski necklaces for z2 + λ/z2",

abstract = "For the family of maps Fλ(z) = zn + λ/zn where n ≥ 3, it is known that there is a McMullen domain surrounding the origin in the parameter plane. This domain is then surrounded by infinitely many “Mandelpinski” necklaces Ik for k = 0, 1, 2, …. These are simple closed curves surrounding the McMullen domain and passing through exactly (n − 2)nk + 1 centers of baby Mandelbrot sets and the same number of centers of Sierpinski holes. When n = 2 there is no such McMullen domain in the parameter plane. However, we show in this paper that there do exist Mandelpinski necklaces Ik in this case. Now these necklaces converge down to the origin. And, consistent with the formula for higher values of n, each Ik passes through the centers of only one Mandelbrot set and one Sierpinski hole.",

keywords = "Complex dynamics, Julia set, Mandelbrot set, Mandelpinski necklace, Rational map, Sierpinski hole",

author = "Daniel Cuzzocreo and Devaney, {Robert L.}",

year = "2016",

month = jan,

day = "1",

doi = "10.1007/978-3-662-52927-0_5",

language = "English (US)",

isbn = "9783662529263",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer New York LLC",

pages = "63--72",

editor = "Cushing, {Jim M.} and Pinto, {Alberto A.} and Saber Elaydi and {i Soler}, {Lluis Alseda}",

booktitle = "Difference Equations, Discrete Dynamical Systems and Applications - ICDEA 2012",

note = "18th International Conference on Difference Equations and Applications, ICDEA 2012 ; Conference date: 23-07-2012 Through 27-07-2012",

}