Λ-symmetries of dynamical systems, Hamiltonian and Lagrangian equations

After a brief survey of the definition and the properties of A-symmetries in the general context of dynamical systems we introduce the notion of "Lambda-constant of motion" for Hamiltonian equations. If the Hamiltonian problem is derived from a A-invariant Lagrangian, it is shown how the Lagrangian Lambda-invariance can be transferred into the Hamiltonian context and shown that the Hamiltonian equations turn out to be Lambda-symmetric. Finally the "partial" (Lagrangian) reduction of the Euler-Lagrange equations is compared with the reduction obtained for the corresponding Hamiltonian equations.