Characterization of symmetries of contact Hamiltonian systems

TL;DR

This paper investigates symmetries in contact Hamiltonian systems, introducing a new vector field decomposition and tensor density framework to characterize symmetries and identify integrals of motion.

Contribution

It presents a novel approach to characterize symmetries in contact Hamiltonian systems using tensor densities and an alternative vector field decomposition.

Findings

Characterization of Cartan symmetries and dynamical similarities in contact Hamiltonian mechanics.

New criteria for assessing the independence of integrals of motion.

Framework enabling the recovery of integrals of motion under specific conditions.

Abstract

This paper explores the relationship between Cartan symmetries, dynamical similarities, and dynamical symmetries in contact Hamiltonian mechanics. By introducing an alternative decomposition of vector fields, we characterize these symmetries and present a novel description in terms of tensor densities. Furthermore, we demonstrate that this framework allows, under specific conditions, for the recovery of integrals of motion. We also establish new criteria to assess their independence.