Dynamical systems with multivalued integrals on a torus

  • V. V. Kozlov


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.


Invariant Measure STEKLOV Institute Morse Function Average Principle Closed Trajectory 
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© Pleiades Publishing, Ltd. 2007

Authors and Affiliations

  • V. V. Kozlov
    • 1
  1. 1.Steklov Institute of MathematicsRussian Academy of SciencesMoscowRussia

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