Characterization of symmetries of contact Hamiltonian systems

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.