2021
DOI: 10.48550/arxiv.2105.00938
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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. * W. Cui expresses his gratitude to the Centre for Mathematical Sciences of Lund University for providing a nice working environment.

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Cited by 2 publications
(6 citation statements)
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“…Combining the methods of [10] with those of the present paper we obtain the following generalization of Corollary 1.3.…”
Section: Introduction and Main Resultssupporting
confidence: 52%
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“…Combining the methods of [10] with those of the present paper we obtain the following generalization of Corollary 1.3.…”
Section: Introduction and Main Resultssupporting
confidence: 52%
“…A result of Kotus and Urbański [27] says that dim J(K) > 2M/(1 + M). It follows from [10, Lemma 2.5] that if N is sufficiently large, then we also have Using the same arguments as in [10] we find that the function…”
Section: Conformal Mappings Of Stripssupporting
confidence: 53%
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