Integrable systems with linear periodic integral for the Lie algebra $\mathrm{e}(3)$

TL;DR

This paper studies integrable systems on the Lie algebra e(3) with linear periodic integrals, analyzing their singularities, bifurcations, and topological properties to deepen understanding of their structure.

Contribution

It provides a detailed topological analysis of integrable systems with linear periodic integrals on e(3), including singularities and bifurcation diagrams, which was not previously explored.

Findings

Classification of singularities of Liouville foliation

Description of bifurcation diagrams of the momentum map

Topological characterization of isoenergy surfaces

Abstract

Integrable systems with a linear periodic integral for the Lie algebra $\mathrm{e}(3)$ are considered. One investigates singulariries of the Liouville foliation, bifurcation diagram of the momentum mapping, transformations of Liouville tori, topology of isoenergy surfaces and other topological properties of such systems.