The Hausdorff dimension of Julia sets of entire functions III

Author:

STALLARD GWYNETH M.

Abstract

It is known that, for a transcendental entire function f, the Hausdorff dimension of the Julia set of f satisfies 1[les ]dim J(f)[les ]2. In this paper we introduce a family of transcendental entire functions fp, K for which the set {dim J(fp, K)[ratio ]0<p, K<∞} has infemum 1 and supremum 2.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Cited by 17 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. On hyperbolic dimension gap for entire functions;Proceedings of the American Mathematical Society;2024-02-02

2. A generalized family of transcendental functions with one dimensional Julia sets;Journal of Difference Equations and Applications;2023-11-13

3. The Hausdorff Dimension of Escaping Sets of Meromorphic Functions in the Speiser Class;International Mathematics Research Notices;2023-07-14

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5. Transcendental Julia sets with fractional packing dimension;Conformal Geometry and Dynamics of the American Mathematical Society;2021-11-16

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