甜点是胡萝卜
Carrots for dessert
摘要：
甜点的胡萝卜是Douady和Hubbard的论文“关于多项式映射”的一节的标题。在这一节中，作者定义了Mandelbrot集M的并矢胡萝卜域的概念，并且更一般地定义了Mandelbrot类家庭。他们评论说，这样的胡萝卜是小的时候，并矢分母是大的，但他们甚至没有试图证明一个精确的这样的声明。本文给出并证明了M周围并矢Carrot场渐近收缩的一个精确命题。同样的证明很容易证明，当分母发散到无穷大时，曼德尔布罗特集M的副本M'在M内部和抛物线曼德尔布罗特集内部的二元装饰会缩小到点。
英文摘要：
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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