A SUMMARY ON SYMMETRIES AND CONSERVED QUANTITIES OF AUTONOMOUS HAMILTONIAN SYSTEMS

被引：10

作者：

Roman-Roy, Narciso ^{[1
]}

机构：

[1] Univ Politecn Cataluna, Dept Math, Edificio C-3,Campus Norte UPC,C Jordi Girona 1, Barcelona 08034, Spain

来源：

JOURNAL OF GEOMETRIC MECHANICS | 2020年 / 12卷 / 03期

关键词：

Symmetries; conserved quantities; Hamiltonian systems; Noether theorem; symplectic manifolds; COMPATIBLE POISSON BRACKETS; NON-NOETHER SYMMETRIES; DYNAMICAL SYMMETRIES; CONSTANTS; MOTION; TODA; THEOREM;

D O I：

10.3934/jgm.2020009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A complete geometric classification of symmetries of autonomous Hamiltonian systems is established; explaining how to obtain their associated conserved quantities in all cases. In particular, first we review well-known results and properties about the symmetries of the Hamiltonian and of the symplectic form and then some new kinds of non-symplectic symmetries and their conserved quantities are introduced and studied.

引用

页码：541 / 551

页数：11

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