A geometric approach to the generalized Noether theorem

Abstract We provide a geometric extension of the generalized Noether theorem for scaling symmetries recently presented by Zhang P-M et al (2020 Eur. Phys. J. Plus 135 223). Our version has several positive features: it is constructed in most natural phase space, allowing to be vector fields on such manifold and associated invariants first integrals motion; direct geometrical proof, paralleling proof standard space Noether’s theorem; automatically yields an inverse applies also large class dissipative systems; finally, allows much larger than just transformations which form Lie algebra, are thus amenable algebraic treatments.