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

Walter Bergweiler, Weiwei Cui

Type: Article

Publication Date: 2022-09-21

Citations: 3

DOI: https://doi.org/10.1007/s00209-022-03142-0

Abstract

We show that for each $d\in (0,2]$ 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 $d$.

Locations

Mathematische Zeitschrift - View - PDF
arXiv (Cornell University) - View - PDF

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Works Cited by This (48)

Action	Title	Year	Authors
+	Fractal measures and ergodic theory of transcendental meromorphic functions	2008	Janina Kotus Mariusz Urbański
+	Dimensions of Julia sets of transcendental meromorphic functions	2008	Gwyneth M. Stallard
+ PDF Chat	Transcendental meromorphic functions with three singular values	2004	Alexandre Erëmenko
+	Iteration of a class of hyperbolic meromorphic functions	1999	P. J. Rippon Gwyneth M. Stallard
+	Dynamics in one complex variable	2000	John Milnor
+	Local connectivity of Julia sets: expository lectures	1992	John Milnor
+	HAUSDORFF DIMENSION AND HAUSDORFF MEASURES OF JULIA SETS OF ELLIPTIC FUNCTIONS	2003	Janina Kotus Mariusz Urbański
+ PDF Chat	Dimensions and Measures in Infinite Iterated Function Systems	1996	R. Daniel Mauldin Mariusz Urbański
+ PDF Chat	On iterates of <i>e</i><sup><i>z</i></sup>	1981	Michał Misiurewicz
+	Iterates of Meromorphic Functions IV: Critically Finite Functions	1992	I. N. Baker Janina Kotus Lü Yinian