{"title":"指数迭代和伯尔集合","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":"{\"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}","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}
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.
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