Solvable submanifolds of tangent bundle and J. Mather generic linear equations

Using J. Mather results on solutions of generic linear equations the smooth solvability of implicit differential systems is investigated. Implicit Hamiltonian systems are considered and algebraic version of J. Mather theorem was applied in this case. For the generalized Hamiltonian systems defined by P.A.M. Dirac on smooth constraints we find the corresponding Poisson-Lie algebras as a basic symplectic invariants of submanifolds in the symplectic space.