{"title":"Exponential Iteration and Borel Sets","authors":"David S. Lipham","doi":"10.1007/s40315-024-00526-7","DOIUrl":null,"url":null,"abstract":"<p>We determine the exact Borel class of escaping sets in the exponential family <span>\\(\\exp (z)+a\\)</span>. We also prove that the sets of non-escaping Julia points for many of these functions are topologically equivalent.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s40315-024-00526-7","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We determine the exact Borel class of escaping sets in the exponential family \(\exp (z)+a\). We also prove that the sets of non-escaping Julia points for many of these functions are topologically equivalent.