Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 132, Pages 57–60 (Mi into165)  

Extension of the concept of invariance and statistically weakly invariant sets of controllable systems

Ya. Yu. Larina, L. I. Rodina

Udmurt State University, Izhevsk
Abstract: We continue the study of statistically invariant and statistically weakly invariant sets with respect to controllable systems and differential inclusions launched by Prof. E. L. Tonkov. We examine properties of such statistical characteristics as the lower $\operatorname{freq}_*(\varphi)$ and upper $\operatorname{freq}^*(\varphi)$ relative frequencies of hitting a solution $\varphi(t)$ of a differential inclusion in a prescribed set. We obtain estimates and conditions of the coincidence of these characteristics for functions whose difference tends to zero at infinity. We also present conditions of statistically weak invariance of a given set of a relatively controllable system.
Keywords: controllable system, dynamical system, attainability set, statistical characteristic, statistically weakly invariant set.
English version:
Journal of Mathematical Sciences (New York), 2018, Volume 230, Issue 5, Pages 703–707
DOI: https://doi.org/10.1007/s10958-018-3773-5
Bibliographic databases:
Document Type: Article
UDC: 517.911, 517.938
MSC: 34A60, 34H05
Language: Russian
Citation: Ya. Yu. Larina, L. I. Rodina, “Extension of the concept of invariance and statistically weakly invariant sets of controllable systems”, Proceedings of International Symposium “Differential Equations–2016”, Perm, May 17-18, 2016, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 132, VINITI, Moscow, 2017, 57–60; J. Math. Sci. (N. Y.), 230:5 (2018), 703–707
Citation in format AMSBIB
\Bibitem{LarRod17}
\by Ya.~Yu.~Larina, L.~I.~Rodina
\paper Extension of the concept of invariance and statistically weakly invariant sets of controllable systems
\inbook Proceedings of International Symposium “Differential Equations–2016”, Perm, May 17-18, 2016
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 132
\pages 57--60
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into165}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3801385}
\zmath{https://zbmath.org/?q=an:1393.34048}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 230
\issue 5
\pages 703--707
\crossref{https://doi.org/10.1007/s10958-018-3773-5}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85044458837}
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