Neil J. Calkin, Eunice Y. S. Chan, Robert M Corless
{"title":"关于Mandelbrot多项式的一些事实和猜想","authors":"Neil J. Calkin, Eunice Y. S. Chan, Robert M Corless","doi":"10.5206/mt.v1i1.14037","DOIUrl":null,"url":null,"abstract":"We show here some facts about the Mandelbrot iterates $z_k(c)$ where $z_0(c)=0$ and $z_{n+1}(c) = z_n^2(c) + c$, which are polynomials in $c$. Some of the facts have proofs, and some other ``\"``facts\" only have experimental evidence but no proof. We invite you to try your hand at filling in the gaps.","PeriodicalId":355724,"journal":{"name":"Maple Transactions","volume":"44 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Some Facts and Conjectures about Mandelbrot Polynomials\",\"authors\":\"Neil J. Calkin, Eunice Y. S. Chan, Robert M Corless\",\"doi\":\"10.5206/mt.v1i1.14037\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show here some facts about the Mandelbrot iterates $z_k(c)$ where $z_0(c)=0$ and $z_{n+1}(c) = z_n^2(c) + c$, which are polynomials in $c$. Some of the facts have proofs, and some other ``\\\"``facts\\\" only have experimental evidence but no proof. We invite you to try your hand at filling in the gaps.\",\"PeriodicalId\":355724,\"journal\":{\"name\":\"Maple Transactions\",\"volume\":\"44 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-10-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Maple Transactions\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5206/mt.v1i1.14037\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Maple Transactions","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5206/mt.v1i1.14037","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Some Facts and Conjectures about Mandelbrot Polynomials
We show here some facts about the Mandelbrot iterates $z_k(c)$ where $z_0(c)=0$ and $z_{n+1}(c) = z_n^2(c) + c$, which are polynomials in $c$. Some of the facts have proofs, and some other ``"``facts" only have experimental evidence but no proof. We invite you to try your hand at filling in the gaps.