Speiser class Julia sets with dimension near one

Simon Albrecht; Christopher J. Bishop

doi:10.1007/s11854-020-0128-1

Speiser class Julia sets with dimension near one

Simon Albrecht
, Christopher J. Bishop

Mathematics

University of Liverpool

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

for any δ > 0 we construct an entire function f with three singular values whose Julia set has Hausdorff dimension at most 1 + δ. Stallard proved that the dimension must be strictly larger than 1 whenever f has a bounded singular set, but no examples with finite singular set and dimension strictly less than 2 were previously known.

Original language	English
Pages (from-to)	49-98
Number of pages	50
Journal	Journal d'Analyse Mathématique
Volume	141
Issue number	1
DOIs	https://doi.org/10.1007/s11854-020-0128-1
State	Published - Sep 2020

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title = "Speiser class Julia sets with dimension near one",

abstract = "for any δ > 0 we construct an entire function f with three singular values whose Julia set has Hausdorff dimension at most 1 + δ. Stallard proved that the dimension must be strictly larger than 1 whenever f has a bounded singular set, but no examples with finite singular set and dimension strictly less than 2 were previously known.",

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AB - for any δ > 0 we construct an entire function f with three singular values whose Julia set has Hausdorff dimension at most 1 + δ. Stallard proved that the dimension must be strictly larger than 1 whenever f has a bounded singular set, but no examples with finite singular set and dimension strictly less than 2 were previously known.

UR - https://www.scopus.com/pages/publications/85095942332

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DO - 10.1007/s11854-020-0128-1

M3 - Article

AN - SCOPUS:85095942332

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JO - Journal d'Analyse Mathématique

JF - Journal d'Analyse Mathématique

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Speiser class Julia sets with dimension near one

Abstract

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