Connecting Anti-integrability to Attractors for Three-Dimensional Quadratic Diffeomorphisms

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-02-06 DOI:10.1137/23m1571897

Amanda E. Hampton, James D. Meiss

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引用次数: 0

Abstract

SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 616-640, March 2024.
Abstract. We previously showed that three-dimensional quadratic diffeomorphisms have anti-integrable (AI) limits that correspond to a quadratic correspondence, a pair of one-dimensional maps. At the AI limit the dynamics is conjugate to a full shift on two symbols. Here we consider a more general AI limit, allowing two parameters of the map to go to infinity. We prove the existence of AI states for each symbol sequence for three cases of the quadratic correspondence: parabolas, ellipses, and hyperbolas. A contraction argument gives parameter domains such that this is a bijection, but the correspondence also is observed to apply more generally. We show that orbits of the original map can be obtained by numerical continuation for a volume-contracting case. These results show that periodic AI states evolve into the observed periodic attractors of the diffeomorphism. We also continue a periodic AI state with a symbol sequence chosen so that it continues to an orbit resembling a chaotic attractor that is a 3D version of the classical 2D Hénon attractor.

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将反不可控性与三维二次微分的吸引力联系起来

SIAM 应用动力系统期刊》第 23 卷第 1 期第 616-640 页，2024 年 3 月。摘要。我们之前证明了三维二次差分变分具有反可积分（AI）极限，它对应于二次对应关系，即一对一维映射。在 AI 极限，动力学共轭于两个符号上的全移。在这里，我们考虑了更一般的 AI 极限，允许映射的两个参数达到无穷大。我们证明了在抛物线、椭圆和双曲线这三种二次对应的情况下，每个符号序列都存在人工智能状态。收缩论证给出了参数域，因此这是一个双射，但也观察到对应关系适用于更广泛的情况。我们证明，在体积收缩的情况下，可以通过数值延续得到原始映射的轨道。这些结果表明，周期性人工智能状态会演化成所观察到的衍射周期性吸引子。我们还用符号序列延续了一个周期性人工智能状态，使其延续到一个类似于混沌吸引子的轨道，而混沌吸引子是经典二维赫农吸引子的三维版本。

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.