# From Newton’s method to exotic basins Part I: The parameter space

Fundamenta Mathematicae (1998)

- Volume: 158, Issue: 3, page 249-288
- ISSN: 0016-2736

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topBarański, Krzysztof. "From Newton’s method to exotic basins Part I: The parameter space." Fundamenta Mathematicae 158.3 (1998): 249-288. <http://eudml.org/doc/212315>.

@article{Barański1998,

abstract = {This is the first part of the work studying the family $\mathfrak \{F\}$ of all rational maps of degree three with two superattracting fixed points. We determine the topological type of the moduli space of $\mathfrak \{F\}$ and give a detailed study of the subfamily $ℱ_2$ consisting of maps with a critical point which is periodic of period 2. In particular, we describe a parabolic bifurcation in $ℱ_2$ from Newton maps to maps with so-called exotic basins.},

author = {Barański, Krzysztof},

journal = {Fundamenta Mathematicae},

keywords = {superattracting fixed points; moduli space; exotic basins; Julia sets; bifurcations; rational maps; Newton maps; parabolic bifurcation; Mandelbrot-like sets},

language = {eng},

number = {3},

pages = {249-288},

title = {From Newton’s method to exotic basins Part I: The parameter space},

url = {http://eudml.org/doc/212315},

volume = {158},

year = {1998},

}

TY - JOUR

AU - Barański, Krzysztof

TI - From Newton’s method to exotic basins Part I: The parameter space

JO - Fundamenta Mathematicae

PY - 1998

VL - 158

IS - 3

SP - 249

EP - 288

AB - This is the first part of the work studying the family $\mathfrak {F}$ of all rational maps of degree three with two superattracting fixed points. We determine the topological type of the moduli space of $\mathfrak {F}$ and give a detailed study of the subfamily $ℱ_2$ consisting of maps with a critical point which is periodic of period 2. In particular, we describe a parabolic bifurcation in $ℱ_2$ from Newton maps to maps with so-called exotic basins.

LA - eng

KW - superattracting fixed points; moduli space; exotic basins; Julia sets; bifurcations; rational maps; Newton maps; parabolic bifurcation; Mandelbrot-like sets

UR - http://eudml.org/doc/212315

ER -

## References

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