A dynamical invariant for Sierpiński cardioid Julia sets

Paul Blanchard, et al. "A dynamical invariant for Sierpiński cardioid Julia sets." Fundamenta Mathematicae 226.3 (2014): 253-277. <http://eudml.org/doc/283134>.

@article{PaulBlanchard2014,
abstract = {For the family of rational maps zⁿ + λ/zⁿ where n ≥ 3, it is known that there are infinitely many small copies of the Mandelbrot set that are buried in the parameter plane, i.e., they do not extend to the outer boundary of this set. For parameters lying in the main cardioids of these Mandelbrot sets, the corresponding Julia sets are always Sierpiński curves, and so they are all homeomorphic to one another. However, it is known that only those cardioids that are symmetrically located in the parameter plane have conjugate dynamics. We produce a dynamical invariant that explains why these maps have different dynamics.},
author = {Paul Blanchard, Daniel Cuzzocreo, Robert L. Devaney, Elizabeth Fitzgibbon, Stefano Silvestri},
journal = {Fundamenta Mathematicae},
keywords = {Sierpiński curve; Julia set; Mandelbrot set; McMullen domain; Cantor necklace},
language = {eng},
number = {3},
pages = {253-277},
title = {A dynamical invariant for Sierpiński cardioid Julia sets},
url = {http://eudml.org/doc/283134},
volume = {226},
year = {2014},
}

TY - JOUR
AU - Paul Blanchard
AU - Daniel Cuzzocreo
AU - Robert L. Devaney
AU - Elizabeth Fitzgibbon
AU - Stefano Silvestri
TI - A dynamical invariant for Sierpiński cardioid Julia sets
JO - Fundamenta Mathematicae
PY - 2014
VL - 226
IS - 3
SP - 253
EP - 277
AB - For the family of rational maps zⁿ + λ/zⁿ where n ≥ 3, it is known that there are infinitely many small copies of the Mandelbrot set that are buried in the parameter plane, i.e., they do not extend to the outer boundary of this set. For parameters lying in the main cardioids of these Mandelbrot sets, the corresponding Julia sets are always Sierpiński curves, and so they are all homeomorphic to one another. However, it is known that only those cardioids that are symmetrically located in the parameter plane have conjugate dynamics. We produce a dynamical invariant that explains why these maps have different dynamics.
LA - eng
KW - Sierpiński curve; Julia set; Mandelbrot set; McMullen domain; Cantor necklace
UR - http://eudml.org/doc/283134
ER -