{"title":"复兴的横列，模微积分和Connes-Kreimer Hopf代数","authors":"Shingo Kamimoto","doi":"10.3792/pjaa.99.013","DOIUrl":null,"url":null,"abstract":"We study the resurgence structure of a formal normalization of a certain vector field to the normal form using “mould calculus” developed by J. Écalle. We also describe the resurgence structure of transseries solutions of a nonlinear ordinary differential equation.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":"179 5-6","pages":"0"},"PeriodicalIF":0.4000,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Resurgent transseries, mould calculus and Connes-Kreimer Hopf algebra\",\"authors\":\"Shingo Kamimoto\",\"doi\":\"10.3792/pjaa.99.013\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the resurgence structure of a formal normalization of a certain vector field to the normal form using “mould calculus” developed by J. Écalle. We also describe the resurgence structure of transseries solutions of a nonlinear ordinary differential equation.\",\"PeriodicalId\":49668,\"journal\":{\"name\":\"Proceedings of the Japan Academy Series A-Mathematical Sciences\",\"volume\":\"179 5-6\",\"pages\":\"0\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2023-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the Japan Academy Series A-Mathematical Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3792/pjaa.99.013\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Japan Academy Series A-Mathematical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3792/pjaa.99.013","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Resurgent transseries, mould calculus and Connes-Kreimer Hopf algebra
We study the resurgence structure of a formal normalization of a certain vector field to the normal form using “mould calculus” developed by J. Écalle. We also describe the resurgence structure of transseries solutions of a nonlinear ordinary differential equation.
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The aim of the Proceedings of the Japan Academy, Series A, is the rapid publication of original papers in mathematical sciences. The paper should be written in English or French (preferably in English), and at most 6 pages long when published. A paper that is a résumé or an announcement (i.e. one whose details are to be published elsewhere) can also be submitted.
The paper is published promptly if once communicated by a Member of the Academy at its General Meeting, which is held monthly except in July and in August.
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