The Hausdorff dimension of Julia sets of meromorphic functions in the Speiser class

Walter Bergweiler; Weiwei Cui

doi:10.1007/s00209-022-03142-0

The Hausdorff dimension of Julia sets of meromorphic functions in the Speiser class

Walter Bergweiler, Weiwei Cui

Matematik LTH

University of Kiel

Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

Sammanfattning

We show that for each d∈ (0 , 2] there exists a meromorphic function f such that the inverse function of f has three singularities and the Julia set of f has Hausdorff dimension d.

Originalspråk	engelska
Sidor (från-till)	2193-2205
Antal sidor	13
Tidskrift	Mathematische Zeitschrift
Volym	302
Nummer	4
DOI	https://doi.org/10.1007/s00209-022-03142-0
Status	Published - 2022 dec.

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© 2022, The Author(s).

Ämnesklassifikation (UKÄ)

Matematisk analys

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title = "The Hausdorff dimension of Julia sets of meromorphic functions in the Speiser class",

abstract = "We show that for each d∈ (0 , 2] there exists a meromorphic function f such that the inverse function of f has three singularities and the Julia set of f has Hausdorff dimension d.",

keywords = "Eremenko–Lyubich class, Fatou set, Hausdorff dimension, Julia set, Meromorphic function, Speiser class",

author = "Walter Bergweiler and Weiwei Cui",

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KW - Eremenko–Lyubich class

KW - Fatou set

KW - Hausdorff dimension

KW - Julia set

KW - Meromorphic function

KW - Speiser class

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The Hausdorff dimension of Julia sets of meromorphic functions in the Speiser class

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