Interesting Esoterica

Carrots for dessert

Article by Petersen, Carsten Lunde and Roesch, Pascale
  • Published in 2010
  • Added on
In the collection
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.

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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}
}