Dynamic classification of escape time Sierpiński curve Julia sets

Robert L. Devaney, and Kevin M. Pilgrim. "Dynamic classification of escape time Sierpiński curve Julia sets." Fundamenta Mathematicae 202.2 (2009): 181-198. <http://eudml.org/doc/283288>.

@article{RobertL2009,
abstract = {For n ≥ 2, the family of rational maps $F_\{λ\}(z) = zⁿ + λ/zⁿ$ contains a countably infinite set of parameter values for which all critical orbits eventually land after some number κ of iterations on the point at infinity. The Julia sets of such maps are Sierpiński curves if κ ≥ 3. We show that two such maps are topologically conjugate on their Julia sets if and only if they are Möbius or anti-Möbius conjugate, and we give a precise count of the number of topological conjugacy classes as a function of n and κ.},
author = {Robert L. Devaney, Kevin M. Pilgrim},
journal = {Fundamenta Mathematicae},
keywords = {Julia set; Sierpiński curve; escape time; conjugacy},
language = {eng},
number = {2},
pages = {181-198},
title = {Dynamic classification of escape time Sierpiński curve Julia sets},
url = {http://eudml.org/doc/283288},
volume = {202},
year = {2009},
}

TY - JOUR
AU - Robert L. Devaney
AU - Kevin M. Pilgrim
TI - Dynamic classification of escape time Sierpiński curve Julia sets
JO - Fundamenta Mathematicae
PY - 2009
VL - 202
IS - 2
SP - 181
EP - 198
AB - For n ≥ 2, the family of rational maps $F_{λ}(z) = zⁿ + λ/zⁿ$ contains a countably infinite set of parameter values for which all critical orbits eventually land after some number κ of iterations on the point at infinity. The Julia sets of such maps are Sierpiński curves if κ ≥ 3. We show that two such maps are topologically conjugate on their Julia sets if and only if they are Möbius or anti-Möbius conjugate, and we give a precise count of the number of topological conjugacy classes as a function of n and κ.
LA - eng
KW - Julia set; Sierpiński curve; escape time; conjugacy
UR - http://eudml.org/doc/283288
ER -