Wiman–Valiron Discs and the Dimension of Julia Sets-Reference-Cited by-同舟云学术

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Wiman–Valiron Discs and the Dimension of Julia Sets

Published:2020-03-03 Issue:12 Volume:2021 Page:9545-9566
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Waterman James¹

Affiliation:

1. School of Mathematics and Statistics, The Open University, Walton Hall, Milton Keynes MK7 6AA, UK

Abstract

Abstract We show that the Hausdorff dimension of the set of points of bounded orbit in the Julia set of a meromorphic map with a simply connected direct tract and a certain restriction on the singular values is strictly greater than one. This result is obtained by proving new results related to Wiman–Valiron theory.

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/imrn/article-pdf/2021/12/9545/38814313/rnaa029.pdf

Reference31 articles.

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2. Hausdorff dimension of hairs and ends for entire maps of finite order;Barański;Math. Proc. Cambridge Philos. Soc.,2008

3. Hyperbolic dimension of Julia sets of meromorphic maps with logarithmic tracts;Barański;Int. Math. Res. Not. IMRN,2009

4. The size of Wiman–Valiron discs;Bergweiler;Complex Var. Elliptic Equ.,2011

5. Iteration of meromorphic functions;Bergweiler;Bull. Amer. Math. Soc. (N.S.),1993

Cited by 1 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. Speiser class Julia sets with dimension near one;Journal d'Analyse Mathématique;2020-09

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