The Birkhoff Normal Form through the Lens of Representation Theory

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Regular and Chaotic Dynamics Pub Date : 2025-08-04 DOI:10.1134/S1560354725520016

Richard Montgomery

引用次数: 0

Abstract

We derive the simplest version of the finite-order Birkhoff normal forms [BNFs], that for area-preserving maps of the plane, using the finite-dimensional representation theory for the group of linear area-preserving maps of that plane and of its circle subgroup. We describe our motivation: the utility of understanding the 3rd-order BNF to obtain KAM stability for non-trivial periodic orbits which arise in celestial mechanics.

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从表征理论的视角看Birkhoff范式

对于平面上的保面积映射，我们利用有限维表示理论，导出了平面上线性保面积映射群及其圆子群的有限阶Birkhoff范式的最简单版本。我们描述了我们的动机：利用理解三阶BNF来获得天体力学中出现的非平凡周期轨道的KAM稳定性。

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

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.