# A dynamical invariant for Sierpiński cardioid Julia sets

Paul Blanchard; Daniel Cuzzocreo; Robert L. Devaney; Elizabeth Fitzgibbon; Stefano Silvestri

Fundamenta Mathematicae (2014)

- Volume: 226, Issue: 3, page 253-277
- ISSN: 0016-2736

## Access Full Article

top## Abstract

top## How to cite

topPaul 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 -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.