{"title":"具有弱 Liouvillean 频率的准周期强迫逻辑图","authors":"Jin Hao Liang, Lin Lin Fu","doi":"10.1007/s10114-024-2692-2","DOIUrl":null,"url":null,"abstract":"<div><p>Consider a class of quasi-periodically forced logistic maps</p><div><div><span>$$\\mathbb{T}\\times[0,1]\\circlearrowleft:(\\theta,x)\\mapsto(\\theta+\\omega,c(\\theta)x(1-x))\\ \\ \\ (\\mathbb{T}=\\mathbb{R}/\\mathbb{Z}),$$</span></div></div><p>where <i>ω</i> is an irrational frequency and <i>α</i>(<i>θ</i>) is a specific bimodal function. We prove that under weak Liouvillean condition on frequency, the strange non-chaotic attractor occurs with negative Lyapunov exponent. This extends the result in [Bjerklov, CMP, 2009].</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 10","pages":"2411 - 2435"},"PeriodicalIF":0.8000,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Quasi-periodically Forced Logistic Map with Weak Liouvillean Frequency\",\"authors\":\"Jin Hao Liang, Lin Lin Fu\",\"doi\":\"10.1007/s10114-024-2692-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Consider a class of quasi-periodically forced logistic maps</p><div><div><span>$$\\\\mathbb{T}\\\\times[0,1]\\\\circlearrowleft:(\\\\theta,x)\\\\mapsto(\\\\theta+\\\\omega,c(\\\\theta)x(1-x))\\\\ \\\\ \\\\ (\\\\mathbb{T}=\\\\mathbb{R}/\\\\mathbb{Z}),$$</span></div></div><p>where <i>ω</i> is an irrational frequency and <i>α</i>(<i>θ</i>) is a specific bimodal function. We prove that under weak Liouvillean condition on frequency, the strange non-chaotic attractor occurs with negative Lyapunov exponent. This extends the result in [Bjerklov, CMP, 2009].</p></div>\",\"PeriodicalId\":50893,\"journal\":{\"name\":\"Acta Mathematica Sinica-English Series\",\"volume\":\"40 10\",\"pages\":\"2411 - 2435\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-05-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematica Sinica-English Series\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10114-024-2692-2\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Sinica-English Series","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10114-024-2692-2","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
where ω is an irrational frequency and α(θ) is a specific bimodal function. We prove that under weak Liouvillean condition on frequency, the strange non-chaotic attractor occurs with negative Lyapunov exponent. This extends the result in [Bjerklov, CMP, 2009].
期刊介绍：
Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.
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