Carrots for dessert

• Published in 2010
• Added on 2012-01-02

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.

Links

• http://arxiv.org/abs/1003.3947
• http://arxiv.org/pdf/1003.3947v1

Other information

BibTeX entry

@article{Petersen2010,
	key = {Petersen2010},
	type = {article},
	title = {Carrots for dessert},
	author = {Petersen, Carsten Lunde and Roesch, Pascale},
	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.},
	comment = {},
	date_added = {2012-01-02},
	date_published = {2010-03-01},
	urls = {http://arxiv.org/abs/1003.3947,http://arxiv.org/pdf/1003.3947v1},
	collections = {Attention-grabbing titles,Food},
	archivePrefix = {arXiv},
	arxivId = {1003.3947},
	eprint = {1003.3947},
	keywords = {Dynamical Systems},
	month = {mar},
	pages = 21,
	url = {http://arxiv.org/abs/1003.3947 http://arxiv.org/pdf/1003.3947v1},
	volume = 0,
	year = 2010,
	primaryClass = {math.DS},
	urldate = {2012-01-02}
}