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Dynamical systems with multivalued integrals on a torus. (English. Russian original) Zbl 1153.37327
Proc. Steklov Inst. Math. 256, 188-205 (2007); translation from Tr. Mat. Inst. Steklova 256, 201-218 (2007).
Summary: Properties of the solutions to differential equations on the torus with a complete set of multivalued first integrals are considered, including the existence of an invariant measure, the averaging principle, and the infiniteness of the number of zeros for integrals of zero-mean functions along trajectories. The behavior of systems with closed trajectories of large period is studied. It is shown that a generic system acquires a limit mixing property as the periods tend to infinity.

MSC:
37C10 Dynamics induced by flows and semiflows
37C55 Periodic and quasi-periodic flows and diffeomorphisms
70H12 Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics
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