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

Fundamenta Mathematicae (2001)

- Volume: 168, Issue: 1, page 1-55
- ISSN: 0016-2736

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topKrzysztof 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 -

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