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Article: Residual julia sets of meromorphic functions

TitleResidual julia sets of meromorphic functions
Authors
KeywordsMathematics Physics
Issue Date2006
PublisherCambridge University Press. The Journal's web site is located at http://journals.cambridge.org/action/displayJournal?jid=PSP
Citation
Mathematical Proceedings Of The Cambridge Philosophical Society, 2006, v. 141 n. 1, p. 113-126 How to Cite?
AbstractIn this paper, we study the residual Julia sets of meromorphic functions. In fact, we prove that if a meromorphic function f belongs to the class S and its Julia set is locally connected, then the residual Julia set of f is empty if and only if its Fatou set F(f) has a completely invariant component or consists of only two components. We also show that if f is a meromorphic function which is not of the form α + (z - α)-keg(z), where k is a natural number, α is a complex number and g is an entire function, then f has buried components provided that f has no completely invariant components and its Julia set J(f) is disconnected. Moreover, if F(f) has an infinitely connected component, then the singleton buried components are dense in J(f). This generalizes a result of Baker and Domínguez. Finally, we give some examples of meromorphic functions with buried points but without any buried components. © 2006 Cambridge Philosophical Society.
Persistent Identifierhttp://hdl.handle.net/10722/44904
ISSN
2015 Impact Factor: 0.534
2015 SCImago Journal Rankings: 1.069
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorTuen Wai, NGen_HK
dc.contributor.authorZheng, JHen_HK
dc.contributor.authorChoi, YYen_HK
dc.date.accessioned2007-10-30T06:13:05Z-
dc.date.available2007-10-30T06:13:05Z-
dc.date.issued2006en_HK
dc.identifier.citationMathematical Proceedings Of The Cambridge Philosophical Society, 2006, v. 141 n. 1, p. 113-126en_HK
dc.identifier.issn0305-0041en_HK
dc.identifier.urihttp://hdl.handle.net/10722/44904-
dc.description.abstractIn this paper, we study the residual Julia sets of meromorphic functions. In fact, we prove that if a meromorphic function f belongs to the class S and its Julia set is locally connected, then the residual Julia set of f is empty if and only if its Fatou set F(f) has a completely invariant component or consists of only two components. We also show that if f is a meromorphic function which is not of the form α + (z - α)-keg(z), where k is a natural number, α is a complex number and g is an entire function, then f has buried components provided that f has no completely invariant components and its Julia set J(f) is disconnected. Moreover, if F(f) has an infinitely connected component, then the singleton buried components are dense in J(f). This generalizes a result of Baker and Domínguez. Finally, we give some examples of meromorphic functions with buried points but without any buried components. © 2006 Cambridge Philosophical Society.en_HK
dc.format.extent177215 bytes-
dc.format.extent51477 bytes-
dc.format.extent1917 bytes-
dc.format.mimetypeapplication/pdf-
dc.format.mimetypeapplication/pdf-
dc.format.mimetypetext/plain-
dc.languageengen_HK
dc.publisherCambridge University Press. The Journal's web site is located at http://journals.cambridge.org/action/displayJournal?jid=PSPen_HK
dc.relation.ispartofMathematical Proceedings of the Cambridge Philosophical Societyen_HK
dc.rightsCambridge Philosophical Society Mathematical Proceedings. Copyright © Cambridge University Press.en_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectMathematics Physicsen_HK
dc.titleResidual julia sets of meromorphic functionsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0305-0041&volume=141&issue=pt 1&spage=113&epage=126&date=2006&atitle=Residual+Julia+Sets+of+Meromorphic+Functionsen_HK
dc.identifier.emailTuen Wai, NG:ntw@maths.hku.hken_HK
dc.identifier.authorityTuen Wai, NG=rp00768en_HK
dc.description.naturepublished_or_final_versionen_HK
dc.identifier.doi10.1017/S0305004106009388en_HK
dc.identifier.scopuseid_2-s2.0-33745700141en_HK
dc.identifier.hkuros125243-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-33745700141&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume141en_HK
dc.identifier.issue1en_HK
dc.identifier.spage113en_HK
dc.identifier.epage126en_HK
dc.identifier.isiWOS:000239349900008-
dc.publisher.placeUnited Kingdomen_HK
dc.identifier.scopusauthoridTuen Wai, NG=7402229732en_HK
dc.identifier.scopusauthoridZheng, JH=7403975674en_HK
dc.identifier.scopusauthoridChoi, YY=14031236600en_HK

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