From Newton's method to exotic basins Part II: Bifurcation of the Mandelbrot-like sets

Krzysztof Barański. "From Newton's method to exotic basins Part II: Bifurcation of the Mandelbrot-like sets." Fundamenta Mathematicae 168.1 (2001): 1-55. <http://eudml.org/doc/282270>.

@article{KrzysztofBarański2001,
abstract = {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.},
author = {Krzysztof Barański},
journal = {Fundamenta Mathematicae},
keywords = {Newton map; Mandelbrot-like set; bifurcation; exotic basin},
language = {eng},
number = {1},
pages = {1-55},
title = {From Newton's method to exotic basins Part II: Bifurcation of the Mandelbrot-like sets},
url = {http://eudml.org/doc/282270},
volume = {168},
year = {2001},
}

TY - JOUR
AU - Krzysztof Barański
TI - From Newton's method to exotic basins Part II: Bifurcation of the Mandelbrot-like sets
JO - Fundamenta Mathematicae
PY - 2001
VL - 168
IS - 1
SP - 1
EP - 55
AB - 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.
LA - eng
KW - Newton map; Mandelbrot-like set; bifurcation; exotic basin
UR - http://eudml.org/doc/282270
ER -