{"title":"Existence of Invariant Curves for Degenerate Quasi-periodic Reversible Mappings","authors":"Peng-Ruei Huang","doi":"10.11650/tjm/220201","DOIUrl":null,"url":null,"abstract":"In this paper we are concerned with the existence of invariant curves of quasi-periodic reversible mappings with higher order degeneracy of the twist condition under the Brjuno–Rüssmann’s non-resonant condition. In the proof we use a new variant of the KAM theory, containing an artificial parameter q, 0 < q < 1, which makes the steps of the KAM iteration infinitely small in the speed of function qε, rather than super exponential function.","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Taiwanese Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.11650/tjm/220201","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
In this paper we are concerned with the existence of invariant curves of quasi-periodic reversible mappings with higher order degeneracy of the twist condition under the Brjuno–Rüssmann’s non-resonant condition. In the proof we use a new variant of the KAM theory, containing an artificial parameter q, 0 < q < 1, which makes the steps of the KAM iteration infinitely small in the speed of function qε, rather than super exponential function.
期刊介绍：
The Taiwanese Journal of Mathematics, published by the Mathematical Society of the Republic of China (Taiwan), is a continuation of the former Chinese Journal of Mathematics (1973-1996). It aims to publish original research papers and survey articles in all areas of mathematics. It will also occasionally publish proceedings of conferences co-organized by the Society. The purpose is to reflect the progress of the mathematical research in Taiwan and, by providing an international forum, to stimulate its further developments. The journal appears bimonthly each year beginning from 2008.
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