Kolmogorov variation: KAM with knobs (à la Kolmogorov)

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

引用次数: 2

Abstract

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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Kolmogorov变体：带旋钮的Kam

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。

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

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