{"title":"Existence of herman rings for meromorphic functions","authors":"P. Domínguez, Núria Fagella †","doi":"10.1080/02781070412331298589","DOIUrl":null,"url":null,"abstract":"We apply the Shishikura surgery construction to transcendental maps in order to obtain examples of meromorphic functions with Herman rings, in a variety of possible arrangements. We give a sharp bound on the maximum possible number of such rings that a meromorphic function may have, in terms of the number of poles. Finally we discuss the possibility of having “unbounded” Herman rings (i.e., with an essential singularity in the boundary), and give some examples of maps with this property.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"85 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2004-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"20","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Complex Variables, Theory and Application: An International Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/02781070412331298589","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 20
Abstract
We apply the Shishikura surgery construction to transcendental maps in order to obtain examples of meromorphic functions with Herman rings, in a variety of possible arrangements. We give a sharp bound on the maximum possible number of such rings that a meromorphic function may have, in terms of the number of poles. Finally we discuss the possibility of having “unbounded” Herman rings (i.e., with an essential singularity in the boundary), and give some examples of maps with this property.
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