Momentum Map and Action-Angle Variables for Nambu Dynamics

TL;DR

This paper explores how momentum maps influence action-angle variables in Nambu dynamics, providing a method to derive new variables for reduced systems, exemplified by the symmetrical top.

Contribution

It introduces a novel approach to generating action-angle variables for Nambu systems via momentum maps, extending classical reduction techniques.

Findings

New action-angle variables for Nambu systems derived from momentum maps

Application demonstrated on the symmetrical top example

Provides a framework for reduction in Nambu dynamics

Abstract

Momentum map is a reduction procedure that reduces the dimension of a Hamiltonian system to the lower ones. It is shown that behavior of the action-angle variables under the momentum map generates the new action-angle variables for the reduced system considered as a Nambu structure. The symmetrical top is given as an illustration.