{"title":"关于预像熵的分形性质","authors":"Teng-San Shih","doi":"10.9734/psij/2021/v25i1230300","DOIUrl":null,"url":null,"abstract":"Fractal dimension for pre-image entropy is introduced for continuous maps throughout this paper. First we show the definition of pre-image entropy dimension of a dynamical system from different topological versions. Then we give those basic propositions of pre-image entropy dimension and the formula for power inequality and forward generator. Relationships among different types of pre-image entropy dimension are studied and an inequality relating them is given. Some basic examples are provided to compare those values of polynomial growth type with the pre-image entropy dimension. After that, this study constructs a symbolic subspace to attain any value between 0 and 1 for pre-image entropy dimension.","PeriodicalId":124795,"journal":{"name":"Physical Science International Journal","volume":"6 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Fractal Properties for Pre-image Entropy\",\"authors\":\"Teng-San Shih\",\"doi\":\"10.9734/psij/2021/v25i1230300\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Fractal dimension for pre-image entropy is introduced for continuous maps throughout this paper. First we show the definition of pre-image entropy dimension of a dynamical system from different topological versions. Then we give those basic propositions of pre-image entropy dimension and the formula for power inequality and forward generator. Relationships among different types of pre-image entropy dimension are studied and an inequality relating them is given. Some basic examples are provided to compare those values of polynomial growth type with the pre-image entropy dimension. After that, this study constructs a symbolic subspace to attain any value between 0 and 1 for pre-image entropy dimension.\",\"PeriodicalId\":124795,\"journal\":{\"name\":\"Physical Science International Journal\",\"volume\":\"6 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-12-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physical Science International Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.9734/psij/2021/v25i1230300\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Science International Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.9734/psij/2021/v25i1230300","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Fractal dimension for pre-image entropy is introduced for continuous maps throughout this paper. First we show the definition of pre-image entropy dimension of a dynamical system from different topological versions. Then we give those basic propositions of pre-image entropy dimension and the formula for power inequality and forward generator. Relationships among different types of pre-image entropy dimension are studied and an inequality relating them is given. Some basic examples are provided to compare those values of polynomial growth type with the pre-image entropy dimension. After that, this study constructs a symbolic subspace to attain any value between 0 and 1 for pre-image entropy dimension.
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