# Carrots for dessert

- Published in 2010
- Added on

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.

## Links

## Other information

- key
- Petersen2010
- type
- article
- date_added
- 2012-01-02
- date_published
- 2010-03-01
- arxivId
- 1003.3947
- keywords
- Dynamical Systems
- pages
- 21

### 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} }