Symmetries and constants of the motion for singular Lagrangian systems (Q1916274)

The merit of this paper is that it presents a coherent survey of the story of symmetries and conservation laws for a number of fairly related yet different situations of degeneracy in the dynamical system. The authors first discuss the classification of symmetries and a Noether-type theorem for presymplectic systems, with special attention for the case of existence of a global dynamics. The results are applied to singular Lagrangian systems and shown to be in good correspondence with the Hamiltonian picture for such systems. Separate short sections are devoted to: the problem of obtaining a reduced second-order system which is equivalent via the Legendre map to the Hamiltonian system on the final constraint submanifold; the rather exotic construction for regular Lagrangian systems of a presymplectic system on the Whitney sum of the tangent and cotangent bundle; the case of a Lagrangian which is linear in the velocities; the reduction of degenerate Lagrangian systems of type II; degenerate systems which admit a presymplectic action of a Lie group. The final section is about precosymplectic systems as a model for the study of symmetries and conservation laws of time-dependent degenerate Lagrangians.