Functions meromorphic outside a small set: completely invariant domains

The theory of Fatou and Julia has been extended in [ 3 ] for the class of functions that are meromorphic outside a sufficiently small, non-empty totally disconnected compact set of essential singularities. For a certain subclass of these functions we study (a) accessibility of boundary points of the...

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Bibliographic Details
Published inComplex variables, theory & application Vol. 49; no. 2; pp. 95 - 100
Main Authors Baker, I.N., Domínguez, P., Herring, M.E.
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 10.02.2004
Subjects
Essential singularities
Fatou set
Julia set
Mathematics Subject Classifications: Primary 37F10
Meromorphic maps
Secondary 37F45
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Summary:The theory of Fatou and Julia has been extended in [ 3 ] for the class of functions that are meromorphic outside a sufficiently small, non-empty totally disconnected compact set of essential singularities. For a certain subclass of these functions we study (a) accessibility of boundary points of the Fatou components and (b) the number of completely invariant domains.
ISSN:0278-1077
1563-5066
DOI:10.1080/02781070310001642620