Scholarlink

<p>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-trivialperiodic orbits which arise in celestial mechanics.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

The Birkhoff Normal Form through the Lens of Representation Theory

  • 期刊论文

  • 发表日期：

    2025年8月4日

查看全文
  • Richard Montgomery

摘要

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-trivialperiodic orbits which arise in celestial mechanics.