{"title":"Flow Map Parameterization Methods for Invariant Tori in Quasi-Periodic Hamiltonian Systems","authors":"Álvaro Fernández-Mora, Alex Haro, J. M. Mondelo","doi":"10.1137/23m1561257","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 127-166, March 2024. <br/> Abstract. The aim of this paper is to present a method to compute parameterizations of partially hyperbolic invariant tori and their invariant bundles in nonautonomous quasi-periodic Hamiltonian systems. We generalize flow map parameterization methods to the quasi-periodic setting. To this end, we introduce the notion of fiberwise isotropic tori and sketch definitions and results on fiberwise symplectic deformations and their moment maps. These constructs are vital to work in a suitable setting and lead to the proofs of “magic cancellations” that guarantee the existence of solutions of cohomological equations. We apply our algorithms in the elliptic restricted three body problem and compute nonresonant 3-dimensional invariant tori and their invariant bundles around the [math] point.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1561257","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 127-166, March 2024. Abstract. The aim of this paper is to present a method to compute parameterizations of partially hyperbolic invariant tori and their invariant bundles in nonautonomous quasi-periodic Hamiltonian systems. We generalize flow map parameterization methods to the quasi-periodic setting. To this end, we introduce the notion of fiberwise isotropic tori and sketch definitions and results on fiberwise symplectic deformations and their moment maps. These constructs are vital to work in a suitable setting and lead to the proofs of “magic cancellations” that guarantee the existence of solutions of cohomological equations. We apply our algorithms in the elliptic restricted three body problem and compute nonresonant 3-dimensional invariant tori and their invariant bundles around the [math] point.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
