Kolmogorov变体：带旋钮的Kam

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-09-13 DOI:10.3934/mine.2023089

M. Sansottera, Veronica Danesi

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引用次数: 2

摘要

在本文中，我们重新考虑了原始的Kolmogorov范式算法[26]，该算法在频率处理上有所变化。与Kolmogorov方法不同的是，我们在归一化过程中没有保持频率固定。此外，我们选择了最终不变环面的频率，并在后验上确定了相应的起始频率。特别是，我们用频率的变化来代替经典的平移步骤。该算法基于Kolmogorov的原始方案，从而利用了Newton-Kantorovich方法的快速收敛性。

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Kolmogorov variation: KAM with knobs (à la Kolmogorov)

In this paper we reconsider the original Kolmogorov normal form algorithm ^[26] with a variation on the handling of the frequencies. At difference with respect to the Kolmogorov approach, we do not keep the frequencies fixed along the normalization procedure. Besides, we select the frequencies of the final invariant torus and determine a posteriori the corresponding starting ones. In particular, we replace the classical translation step with a change of the frequencies. The algorithm is based on the original scheme of Kolmogorov, thus exploiting the fast convergence of the Newton-Kantorovich method.

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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.