Remark on conservation laws associated with non-Noether symmetries

TL;DR

This paper explores the geometric relationship between non-Noether symmetries and conservation laws in Hamiltonian systems, showing that integrals of motion are in involution under certain conditions.

Contribution

It demonstrates that integrals of motion from non-Noether symmetries are in involution if the symmetry generator satisfies a Yang-Baxter equation.

Findings

Integrals of motion from non-Noether symmetries are in involution.

The involution condition is linked to a Yang-Baxter equation.

Geometric aspects of non-Noether symmetries are elucidated.

Abstract

In the present paper geometric aspects of relationship between non-Noether symmetries and conservation laws in Hamiltonian systems is discussed. It is shown that integrals of motion associated with continuous non-Noether symmetry are in involution whenever generator of the symmetry satisfies certain Yang-Baxter equation.