{"title":"Special functions created by Borel-Laplace transform of Hénon map","authors":"C. Matsuoka, K. Hiraide","doi":"10.3934/ERA.2011.18.1","DOIUrl":null,"url":null,"abstract":"We present a novel class of functions that can describe the stable and unstable manifolds of the Henon map. We propose an algorithm to construct these functions by using the Borel-Laplace transform. Neither linearization nor perturbation is applied in the construction, and the obtained functions are exact solutions of the Henon map. We also show that it is possible to depict the chaotic attractor of the map by using one of these functions without explicitly using the properties of the attractor.","PeriodicalId":53151,"journal":{"name":"Electronic Research Announcements in Mathematical Sciences","volume":"18 1","pages":"1-11"},"PeriodicalIF":0.0000,"publicationDate":"2011-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Research Announcements in Mathematical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/ERA.2011.18.1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 3
Abstract
We present a novel class of functions that can describe the stable and unstable manifolds of the Henon map. We propose an algorithm to construct these functions by using the Borel-Laplace transform. Neither linearization nor perturbation is applied in the construction, and the obtained functions are exact solutions of the Henon map. We also show that it is possible to depict the chaotic attractor of the map by using one of these functions without explicitly using the properties of the attractor.
期刊介绍：
Electronic Research Archive (ERA), formerly known as Electronic Research Announcements in Mathematical Sciences, rapidly publishes original and expository full-length articles of significant advances in all branches of mathematics. All articles should be designed to communicate their contents to a broad mathematical audience and must meet high standards for mathematical content and clarity. After review and acceptance, articles enter production for immediate publication.
ERA is the continuation of Electronic Research Announcements of the AMS published by the American Mathematical Society, 1995—2007
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