Geodesic
Dynamical Systems with Multivalued Integrals on a Torus
Informatics and Automation, Dynamical systems and optimization, Tome 256 (2007), pp. 201-218

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TRSPY_2007_256_a9,
     author = {V. V. Kozlov},
     title = {Dynamical {Systems} with {Multivalued} {Integrals} on a {Torus}},
     journal = {Informatics and Automation},
     pages = {201--218},
     publisher = {mathdoc},
     volume = {256},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2007_256_a9/}
}
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V. V. Kozlov. Dynamical Systems with Multivalued Integrals on a Torus. Informatics and Automation, Dynamical systems and optimization, Tome 256 (2007), pp. 201-218. http://geodesic.mathdoc.fr/item/TRSPY_2007_256_a9/