归一化流程

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED Regular and Chaotic Dynamics Pub Date : 2023-10-20 DOI:10.1134/S1560354723040160

Dmitry V. Treschev

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引用次数: 1

摘要

我们提出了一种新的方法来研究非共振椭圆奇异点附近哈密顿系统的正规形式理论。我们考虑在原点有这样一个平衡位置的所有哈密顿函数的空间，并在这个空间中构造一个微分方程。这个方程的解将哈密顿函数推向它们的正规形式。沿着该方程的流动的偏移对应于规范坐标的变化。因此，我们有一个连续的规范化程序。该理论的形式方面没有任何困难。和往常一样，级数的解析方面和收敛问题是不平凡的。

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Normalization Flow

We propose a new approach to the theory of normal forms for Hamiltonian systems near a nonresonant elliptic singular point. We consider the space of all Hamiltonian functions with such an equilibrium position at the origin and construct a differential equation in this space. Solutions of this equation move Hamiltonian functions towards their normal forms. Shifts along the flow of this equation correspond to canonical coordinate changes. So, we have a continuous normalization procedure. The formal aspect of the theory presents no difficulties. As usual, the analytic aspect and the problems of convergence of series are nontrivial.

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来源期刊

Regular and Chaotic Dynamics 物理-力学

CiteScore

2.50

自引率

7.10%

发文量

审稿时长

>12 weeks

期刊介绍： Regular and Chaotic Dynamics (RCD) is an international journal publishing original research papers in dynamical systems theory and its applications. Rooted in the Moscow school of mathematics and mechanics, the journal successfully combines classical problems, modern mathematical techniques and breakthroughs in the field. Regular and Chaotic Dynamics welcomes papers that establish original results, characterized by rigorous mathematical settings and proofs, and that also address practical problems. In addition to research papers, the journal publishes review articles, historical and polemical essays, and translations of works by influential scientists of past centuries, previously unavailable in English. Along with regular issues, RCD also publishes special issues devoted to particular topics and events in the world of dynamical systems.