Geodesic
Extension of the concept of invariance and statistically weakly invariant sets of controllable systems
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of International Symposium “Differential Equations–2016”, Perm, May 17-18, 2016, Tome 132 (2017), pp. 57-60.

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

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. 
@article{INTO_2017_132_a12,
     author = {Ya. Yu. Larina and L. I. Rodina},
     title = {Extension of the concept of invariance and statistically weakly invariant sets of controllable systems},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {57--60},
     publisher = {mathdoc},
     volume = {132},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2017_132_a12/}
}
TY  - JOUR
AU  - Ya. Yu. Larina
AU  - L. I. Rodina
TI  - Extension of the concept of invariance and statistically weakly invariant sets of controllable systems
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2017
SP  - 57
EP  - 60
VL  - 132
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2017_132_a12/
LA  - ru
ID  - INTO_2017_132_a12
ER  - 
%0 Journal Article
%A Ya. Yu. Larina
%A L. I. Rodina
%T Extension of the concept of invariance and statistically weakly invariant sets of controllable systems
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2017
%P 57-60
%V 132
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2017_132_a12/
%G ru
%F INTO_2017_132_a12
Ya. Yu. Larina; L. I. Rodina. Extension of the concept of invariance and statistically weakly invariant sets of controllable systems. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of International Symposium “Differential Equations–2016”, Perm, May 17-18, 2016, Tome 132 (2017), pp. 57-60. http://geodesic.mathdoc.fr/item/INTO_2017_132_a12/