Evgeniy Tonkov

    1, Universitetskaya str., Izhevsk 426034
    Department of Differential Equations, Udmurt State University


    Rodina L. I., Tonkov E. L.
    In the terms of Lyapunov functions we obtain the conditions that allow to estimate the relative frequency of occurrence of the attainable set of a controllable system in a given set $\mathfrak{M}$. The set $\mathfrak{M}$ is called statistically invariant if the relative frequency of occurrence in $\mathfrak{M}$ is equal to one. We also derive the conditions of the statistically weak invariance of $\mathfrak{M}$ with respect to controllable system, that is, for every initial point from $\mathfrak{M}$, at least one solution of the controllable system is statistically invariant. We obtain the conditions for the attainable set to be non-wandering as well as the conditions of existence of the minimal attraction center.
    Keywords: controllable systems, dynamical systems, differential inclusions, attainability, invariance, non-wandering, recurrence
    Citation: Rodina L. I., Tonkov E. L.,  Statistical characteristics of attainable set of controllable system, non-wandering, and minimal attraction center, Rus. J. Nonlin. Dyn., 2009, Vol. 5, No. 2, pp.  265-288

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