Generic Hamiltonian Dynamical Systems are Neither Integrable nor Ergodic

Lawrence Markus · Kenneth Ray Meyer

jan. 1974 · American Mathematical Society: Memoirs of the American Mathematical Society Bok 144 · American Mathematical Soc.

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This memoir gives an introduction to Hamiltonian dynamical systems on symplectic manifolds, including definitions of Hamiltonian vector fields, Poisson brackets, integrals of motion, complete integrability, and ergodicity. A particularly complete treatment of action-angle coordinates is given. Historical background into the question of ergodicity and integrability in Hamiltonian systems is also given.