{"title":"tue - morse序列光谱测量的多重分形分析:周期轨道方法","authors":"Z. Bai","doi":"10.1088/0305-4470/39/35/002","DOIUrl":null,"url":null,"abstract":"The Fourier spectral density of the Thue–Morse sequence is reinterpreted as the invariant measure of a stochastic dynamical system. Based on this fact, its generalized (Rényi) dimension and f(α) statistics are calculated with high precision by cycle expansions of spectral determinant and dynamical zeta function. αq at integer values of q are also computed in an operator scheme and the asymptotic result in the large-q limit is derived.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2006-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Multifractal analysis of the spectral measure of the Thue–Morse sequence: a periodic orbit approach\",\"authors\":\"Z. Bai\",\"doi\":\"10.1088/0305-4470/39/35/002\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The Fourier spectral density of the Thue–Morse sequence is reinterpreted as the invariant measure of a stochastic dynamical system. Based on this fact, its generalized (Rényi) dimension and f(α) statistics are calculated with high precision by cycle expansions of spectral determinant and dynamical zeta function. αq at integer values of q are also computed in an operator scheme and the asymptotic result in the large-q limit is derived.\",\"PeriodicalId\":87442,\"journal\":{\"name\":\"Journal of physics A: Mathematical and general\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2006-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of physics A: Mathematical and general\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1088/0305-4470/39/35/002\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of physics A: Mathematical and general","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1088/0305-4470/39/35/002","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Multifractal analysis of the spectral measure of the Thue–Morse sequence: a periodic orbit approach
The Fourier spectral density of the Thue–Morse sequence is reinterpreted as the invariant measure of a stochastic dynamical system. Based on this fact, its generalized (Rényi) dimension and f(α) statistics are calculated with high precision by cycle expansions of spectral determinant and dynamical zeta function. αq at integer values of q are also computed in an operator scheme and the asymptotic result in the large-q limit is derived.