Canonoid transformations and master symmetries

TL;DR

This paper explores canonoid transformations and master symmetries in Hamiltonian systems using geometric formalism, analyzing their properties, relations to constants of motion, and underlying algebraic structures.

Contribution

It provides a detailed geometric analysis of canonoid transformations and master symmetries, highlighting their roles in conserved quantities and system symmetries.

Findings

Canonoid transformations are characterized using boundary and coboundary operators.

Master symmetries are linked to the existence of conserved quantities.

The geometric formalism clarifies the structure of symmetries in Hamiltonian systems.

Abstract

Different types of transformations of a dynamical system, that are compatible with the Hamiltonian structure, are discussed making use of a geometric formalism. Firstly, the case of canonoid transformations is studied with great detail and then the properties of master symmetries are also analyzed. The relations between the existence of constants of motion and the properties of canonoid symmetries is discussed making use of a family of boundary and coboundary operators.