2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57200We disscuss some geometric aspects of the concept of non-Noether symmetry. It is shown that in regular Hamiltonian systems such a symmetry canonically leads to a Lax pair on the algebra of linear operators on cotangent bundle over the phase space. Correspondence between the non-Noether symmetries and other wide spread geometric methods of generating conservation laws such as bi-Hamiltonian formalism, bidifferential calculi and Frolicher-Nijenhuis geometry is considered. It is proved that the integrals of motion associated with the continuous non-Noether symmetry are in involution whenever the generator of the symmetry satisfies a certain Yang-Baxter type equation.LaTeX 2e article, 16 pages, no figures, revised versionMathematical PhysicsSymplectic Geometry70H33, 70H06, 53Z05text