2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/230279In this paper we consider the relation between symmetries and first integrals of canonical Hamiltonian equations. Based on a newly established identity (which is an analog of well known Noether's identity for Lagrangian approach), this approach provides a simple and clear way to construct first integrals with the help of symmetries of a Hamiltonian. The approach is illustrated by a number of examples, including equations of the three-dimensional Kepler motion.Mathematical PhysicsDynamical Systems70H05, 70H33text