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The Hausdorff Dimension of Julia Sets of Meromorphic Functions
Author(s) -
Stallard Gwyneth M.
Publication year - 1994
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/49.2.281
Subject(s) - julia set , meromorphic function , hausdorff dimension , mathematics , transcendental number , dimension (graph theory) , pure mathematics , class (philosophy) , hausdorff space , entire function , mathematical analysis , computer science , artificial intelligence
We consider the class of transcendental meromorphic functions which have at least one pole and are not conjugate to a self‐map of C∗. We show that the Hausdorff dimension of the Julia set of such a function satisfies 0 < dim J ( f ) ⩽ 2 and this result is sharp.