{"title":"一维连续体超空间中的递归和熵","authors":"Domagoj Jelić, Piotr Oprocha","doi":"10.4064/fm235-4-2023","DOIUrl":null,"url":null,"abstract":"We show that if $G$ is a topological graph, and $f\\colon G\\to G$ is a continuous map, then the induced map $\\tilde {f}$ defined on the hyperspace $C(G)$ of all connected subsets of $G$ by the natural formula $\\tilde {f}(C)=f(C)$ carries the same entro","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On recurrence and entropy in the hyperspace of continua in dimension one\",\"authors\":\"Domagoj Jelić, Piotr Oprocha\",\"doi\":\"10.4064/fm235-4-2023\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that if $G$ is a topological graph, and $f\\\\colon G\\\\to G$ is a continuous map, then the induced map $\\\\tilde {f}$ defined on the hyperspace $C(G)$ of all connected subsets of $G$ by the natural formula $\\\\tilde {f}(C)=f(C)$ carries the same entro\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4064/fm235-4-2023\",\"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":"1085","ListUrlMain":"https://doi.org/10.4064/fm235-4-2023","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On recurrence and entropy in the hyperspace of continua in dimension one
We show that if $G$ is a topological graph, and $f\colon G\to G$ is a continuous map, then the induced map $\tilde {f}$ defined on the hyperspace $C(G)$ of all connected subsets of $G$ by the natural formula $\tilde {f}(C)=f(C)$ carries the same entro
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