{"title":"孤立二阶数","authors":"Fernando Argentieri, Luigi Chierchia","doi":"10.1134/S156035472455001X","DOIUrl":null,"url":null,"abstract":"<div><p>In this note, we discuss the topology of Diophantine numbers, giving simple explicit\nexamples of Diophantine isolated numbers (among those with the same Diophantine constants),\nshowing that <i>Diophantine sets are not always Cantor sets</i>.</p><p>General properties of isolated Diophantine numbers are also briefly discussed.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 and Dmitry Treschev)","pages":"536 - 540"},"PeriodicalIF":0.8000,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1134/S156035472455001X.pdf","citationCount":"0","resultStr":"{\"title\":\"Isolated Diophantine Numbers\",\"authors\":\"Fernando Argentieri, Luigi Chierchia\",\"doi\":\"10.1134/S156035472455001X\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this note, we discuss the topology of Diophantine numbers, giving simple explicit\\nexamples of Diophantine isolated numbers (among those with the same Diophantine constants),\\nshowing that <i>Diophantine sets are not always Cantor sets</i>.</p><p>General properties of isolated Diophantine numbers are also briefly discussed.</p></div>\",\"PeriodicalId\":752,\"journal\":{\"name\":\"Regular and Chaotic Dynamics\",\"volume\":\"29 and Dmitry Treschev)\",\"pages\":\"536 - 540\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-07-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1134/S156035472455001X.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Regular and Chaotic Dynamics\",\"FirstCategoryId\":\"4\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S156035472455001X\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Regular and Chaotic Dynamics","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1134/S156035472455001X","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
In this note, we discuss the topology of Diophantine numbers, giving simple explicit
examples of Diophantine isolated numbers (among those with the same Diophantine constants),
showing that Diophantine sets are not always Cantor sets.
General properties of isolated Diophantine numbers are also briefly discussed.
期刊介绍：
Regular and Chaotic Dynamics (RCD) is an international journal publishing original research papers in dynamical systems theory and its applications. Rooted in the Moscow school of mathematics and mechanics, the journal successfully combines classical problems, modern mathematical techniques and breakthroughs in the field. Regular and Chaotic Dynamics welcomes papers that establish original results, characterized by rigorous mathematical settings and proofs, and that also address practical problems. In addition to research papers, the journal publishes review articles, historical and polemical essays, and translations of works by influential scientists of past centuries, previously unavailable in English. Along with regular issues, RCD also publishes special issues devoted to particular topics and events in the world of dynamical systems.
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