Singular lagrangians: some geometric structures along the Legendre map
  New geometric structures that relate the lagrangian and hamiltonian formalisms defined upon a singular lagrangian are presented. Several vector fields are constructed in velocity space that give new and precise answers to several topics like the projectability of a vector field to a hamiltonian vector field, the computation of the kernel of the presymplectic form of lagrangian formalism, the construction of the lagrangian dynamical vector fields, and the characterisation of dynamical symmetries. 
Xavier Gracia (Technical University of Catalonia) and Josep M. Pons   (University of Barcelona)