# Carrots for dessert

• Published in 2010
In the collections
Carrots for dessert is the title of a section of the paper On polynomial-like mappings' by Douady and Hubbard. In that section the authors define a notion of dyadic carrot fields of the Mandelbrot set M and more generally for Mandelbrot like families. They remark that such carrots are small when the dyadic denominator is large, but they do not even try to prove a precise such statement. In this paper we formulate and prove a precise statement of asymptotic shrinking of dyadic Carrot-fields around M. The same proof carries readily over to show that the dyadic decorations of copies M' of the Mandelbrot set M inside M and inside the parabolic Mandelbrot set shrink to points when the denominator diverge to infinity.

## Other information

arxivId
1003.3947
keywords
Dynamical Systems
pages
21

### BibTeX entry

@article{Petersen2010,
abstract = {Carrots for dessert is the title of a section of the paper On polynomial-like mappings' by Douady and Hubbard. In that section the authors define a notion of dyadic carrot fields of the Mandelbrot set M and more generally for Mandelbrot like families. They remark that such carrots are small when the dyadic denominator is large, but they do not even try to prove a precise such statement. In this paper we formulate and prove a precise statement of asymptotic shrinking of dyadic Carrot-fields around M. The same proof carries readily over to show that the dyadic decorations of copies M' of the Mandelbrot set M inside M and inside the parabolic Mandelbrot set shrink to points when the denominator diverge to infinity.},
archivePrefix = {arXiv},
arxivId = {1003.3947},
author = {Petersen, Carsten Lunde and Roesch, Pascale},
eprint = {1003.3947},
keywords = {Dynamical Systems},
month = {mar},
pages = 21,
title = {Carrots for dessert},
url = {http://arxiv.org/abs/1003.3947 http://arxiv.org/pdf/1003.3947v1},
volume = 0,
year = 2010,
primaryClass = {math.DS},
urldate = {2012-01-02},
collections = {Attention-grabbing titles,Food}
}