Normal form for lower dimensional elliptic tori in Hamiltonian systems

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-10-19 DOI:10.3934/mine.2022051

Chiara Caracciolo

引用次数: 2

Abstract

We give a proof of the convergence of an algorithm for the construction of lower dimensional elliptic tori in nearly integrable Hamiltonian systems. The existence of such invariant tori is proved by leading the Hamiltonian to a suitable normal form. In particular, we adapt the procedure described in a previous work by Giorgilli and co-workers, where the construction was made so as to be used in the context of the planetary problem. We extend the proof of the convergence to the cases in which the two sets of frequencies, describing the motion along the torus and the transverse oscillations, have the same order of magnitude.

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哈密顿系统中低维椭圆环面的范式

我们证明了在几乎可积的哈密顿系统中构造低维椭圆环面的一个算法的收敛性。通过将哈密顿量引入一个合适的正规形式，证明了这种不变复曲面的存在。特别是，我们采用了Giorgilli及其同事在以前的工作中描述的程序，在那里进行了构造，以便在行星问题的背景下使用。我们将收敛性的证明扩展到描述沿环面运动和横向振荡的两组频率具有相同数量级的情况。

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.