SYMMETRIES AND REGULAR BEHAVIOR OF HAMILTONIAN-SYSTEMS

The behavior of the phase trajectories of the Hamilton equations is co mmonly classified as regular and chaotic. Regularity is usually relate d to the condition for complete integrability, i.e., a Hamiltonian sys tem with n degrees of freedom has n independent integrals in involutio n. If at the same time the simultaneous integral manifolds are compact , the solutions of the Hamilton equations are quasiperiodic. In partic ular, the entropy of the Hamiltonian phase flow of a completely integr able system is zero. It is found that there is a broader class of Hami ltonian systems that do not show signs of chaotic behavior. These are systems that allow n commuting ''Lagrangian'' vector fields, i.e., the symplectic 2-form on each pair of such fields is zero. They include, in particular, Hamiltonian systems with multivalued integrals. (C) 199 6 American Institute of Physics.