 Basic differential geometry (manifolds, definition and basic properties of vector fields and differential forms and operations over them)  Hamiltonian systems (the Poisson structures and their properties, the Darboux theorem, Hamiltonian, the Hamilton equations, integrals of motion, complete integrability and the Liouville theorem, bihamiltonian systems)  The HamiltonJacobi theory and related issues (complete integral, the Jacobi integration method, the HamiltonJacobi equation, separation of variables, the actionangle variables)


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