Flow Map Parameterization Methods for Invariant Tori in Quasi-Periodic Hamiltonian Systems

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-01-12 DOI:10.1137/23m1561257

Álvaro Fernández-Mora, Alex Haro, J. M. Mondelo

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.

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准周期哈密顿系统中不变环的流图参数化方法

SIAM 应用动力系统期刊》，第 23 卷第 1 期，第 127-166 页，2024 年 3 月。摘要本文旨在提出一种计算非自治准周期哈密顿系统中部分双曲不变环及其不变束参数化的方法。我们将流图参数化方法推广到准周期设置中。为此，我们引入了纤向各向同性环的概念，并简要介绍了纤向交映变形及其矩图的定义和结果。这些构造对于在合适的环境中工作至关重要，并导致了 "神奇抵消 "的证明，从而保证了同调方程解的存在性。我们在椭圆受限三体问题中应用了我们的算法，并计算了[math]点周围的非共振三维不变环及其不变束。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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.