This is a continuation of the work [Ba] dealing with the family of all cubic rational maps with two supersinks. We prove the existence of the following parabolic bifurcation of Mandelbrot-like sets in the parameter space of this family. Starting from a Mandelbrot-like set in cubic Newton maps and changing parameters in a continuous way, we construct a path of Mandelbrot-like sets ending in the family of parabolic maps with a fixed point of multiplier 1. Then it bifurcates into two paths of Mandelbrot-like sets, contained respectively in the set of maps with exotic or non-exotic basins. The non-exotic path ends at a Mandelbrot-like set in cubic polynomials.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm168-1-1,
author = {Krzysztof Bara\'nski},
title = {From Newton's method to exotic basins Part II: Bifurcation of the Mandelbrot-like sets},
journal = {Fundamenta Mathematicae},
volume = {167},
year = {2001},
pages = {1-55},
zbl = {0987.37037},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm168-1-1}
}
Krzysztof Barański. From Newton's method to exotic basins Part II: Bifurcation of the Mandelbrot-like sets. Fundamenta Mathematicae, Tome 167 (2001) pp. 1-55. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm168-1-1/