幂映射的插值

IF 1.3 2区数学 Q1 MATHEMATICS

Revista Matematica Iberoamericana Pub Date : 2021-01-11 DOI:10.4171/rmi/1359

Jack Burkart, K. Lazebnik

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引用次数: 2

摘要

．设(M j)∞j =1∈N， (r j)∞j =1∈r +是满足某种温和增长率条件的递增序列。我们证明了一个完整的函数f: C→C在大环空{z∈C: r j·exp(π/M j)≤| z |≤r j +1}中的行为是由z (cid:55)→z M j的扰动重标给出的，使得f的唯一奇异值是±r M j j的重标。我们描述了整个函数动力学的几个应用。

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Interpolation of power mappings

. Let ( M j ) ∞ j =1 ∈ N and ( r j ) ∞ j =1 ∈ R + be increasing sequences satisfying some mild rate of growth conditions. We prove that there is an entire function f : C → C whose behavior in the large annuli { z ∈ C : r j · exp( π/M j ) ≤ | z | ≤ r j +1 } is given by a perturbed rescaling of z (cid:55)→ z M j , such that the only singular values of f are rescalings of ± r M j j . We describe several applications to the dynamics of entire functions.

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来源期刊

Revista Matematica Iberoamericana 数学-数学

CiteScore

2.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Revista Matemática Iberoamericana publishes original research articles on all areas of mathematics. Its distinguished Editorial Board selects papers according to the highest standards. Founded in 1985, Revista is a scientific journal of Real Sociedad Matemática Española.