Immediate Renormalization of Cubic Complex Polynomials with Empty Rational Lamination

IF 0.6 4区数学 Q3 MATHEMATICS

Moscow Mathematical Journal Pub Date : 2023-08-29 DOI:10.17323/1609-4514-2023-23-4-441-461

A. Blokh, L. Oversteegen, V. Timorin

引用次数: 0

Abstract

A cubic polynomial $P$ with a non-repelling fixed point $b$ is said to be immediately renormalizable if there exists a (connected) QL invariant filled Julia set $K^*$ such that $b\in K^*$. In that case, exactly one critical point of $P$ does not belong to $K^*$. We show that if, in addition, the Julia set of $P$ has no (pre)periodic cutpoints, then this critical point is recurrent.

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空有理层叠立方复多项式的立即重正化

如果存在一个（连通的）QL不变填充朱利亚集$K^*$，使得$b/in K^*$，那么具有非排斥定点$b$的立方多项式$P$就可以说是立即可重正化的。在这种情况下，$P$ 恰好有一个临界点不属于 $K^*$。我们证明，如果此外 $P$ 的 Julia 集没有（前）周期切点，那么这个临界点就是经常出现的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Moscow Mathematical Journal 数学-数学

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Moscow Mathematical Journal (MMJ) is an international quarterly published (paper and electronic) by the Independent University of Moscow and the department of mathematics of the Higher School of Economics, and distributed by the American Mathematical Society. MMJ presents highest quality research and research-expository papers in mathematics from all over the world. Its purpose is to bring together different branches of our science and to achieve the broadest possible outlook on mathematics, characteristic of the Moscow mathematical school in general and of the Independent University of Moscow in particular. An important specific trait of the journal is that it especially encourages research-expository papers, which must contain new important results and include detailed introductions, placing the achievements in the context of other studies and explaining the motivation behind the research. The aim is to make the articles — at least the formulation of the main results and their significance — understandable to a wide mathematical audience rather than to a narrow class of specialists.