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Article: Permutable entire functions and their Julia sets

TitlePermutable entire functions and their Julia sets
Authors
Ng, TW
Issue Date2001
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, 2001, v. 131 n. 1, p. 129-138 How to Cite?
DOI: http://dx.doi.org/10.1017/S0305004101005084
AbstractIn 1922-23, Julia and Fatou proved that any 2 rational functions f and g of degree at least 2 such that f(g(z)) = g(f(z)), have the same Julia set. Baker then asked whether the result remains true for nonlinear entire functions. In this paper, we shall show that the answer to Baker's question is true for almost all nonlinear entire functions. The method we use is useful for solving functional equations. It actually allows us to find out all the entire functions g which permute with a given f which belongs to a very large class of entire functions. © 2001 Cambridge Philosophical Society.
Persistent Identifierhttp://hdl.handle.net/10722/75206
ISSN
0305-0041
2023 Impact Factor: 0.6
2023 SCImago Journal Rankings: 0.929
References
References in Scopus

 

DC FieldValueLanguage
dc.contributor.authorNg, TWen_HK
dc.date.accessioned2010-09-06T07:08:57Z-
dc.date.available2010-09-06T07:08:57Z-
dc.date.issued2001en_HK
dc.identifier.citationMathematical Proceedings Of The Cambridge Philosophical Society, 2001, v. 131 n. 1, p. 129-138en_HK
dc.identifier.issn0305-0041en_HK
dc.identifier.urihttp://hdl.handle.net/10722/75206-
dc.description.abstractIn 1922-23, Julia and Fatou proved that any 2 rational functions f and g of degree at least 2 such that f(g(z)) = g(f(z)), have the same Julia set. Baker then asked whether the result remains true for nonlinear entire functions. In this paper, we shall show that the answer to Baker's question is true for almost all nonlinear entire functions. The method we use is useful for solving functional equations. It actually allows us to find out all the entire functions g which permute with a given f which belongs to a very large class of entire functions. © 2001 Cambridge Philosophical Society.en_HK
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.rightsMathematical Proceedings of the Cambridge Philosophical Society. Copyright © Cambridge University Press.en_HK
dc.titlePermutable entire functions and their Julia setsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0305-0041&volume=131&issue=1&spage=129&epage=138&date=2001&atitle=Permutable+entire+functions+and+their+Julia+Setsen_HK
dc.identifier.emailNg, TW:ntw@maths.hku.hken_HK
dc.identifier.authorityNg, TW=rp00768en_HK
dc.description.naturepublished_or_final_version-
dc.identifier.doi10.1017/S0305004101005084-
dc.identifier.scopuseid_2-s2.0-23044526658en_HK
dc.identifier.hkuros66768en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-23044526658&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume131en_HK
dc.identifier.issue1en_HK
dc.identifier.spage129en_HK
dc.identifier.epage138en_HK
dc.publisher.placeUnited Kingdomen_HK
dc.identifier.scopusauthoridNg, TW=7402229732en_HK
dc.identifier.issnl0305-0041-

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