Symmetries, psudosymmetries and conservation laws in Lagrangian and   Hamiltonian $k$-symplectic formalisms
  In this paper we will present Lagrangian and Hamiltonian $k$-symplectic formalisms, we will recall the notions of symmetry and conservation law and we will define the notion of pseudosymmetry as a natural extension of symmetry. Using symmetries and pseudosymmetries, without the help of a Noether type theorem, we will obtain new kinds of conservation laws for $k$-symplectic Hamiltonian systems and $k$-symplectic Lagrangian systems. 
Florian Munteanu
math.DG math-ph math.MP