Geodesic
The convergence of Euler's broken lines
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 2 (2008), pp. 163-164 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider the convergence of Euler's broken lines to trajectories of the system under Carathéodory's conditions. We introduce a pseudometric on the set of closed subsets of the time segment, taking into account the system. We prove that the convergence of partitions guarantees the convergence of Euler's broken lines to the funnel of solutions of the system. 
@article{VUU_2008_2_a52,
     author = {D. V. Khlopin},
     title = {The convergence of {Euler's} broken lines},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {163--164},
     year = {2008},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2008_2_a52/}
}
TY  - JOUR
AU  - D. V. Khlopin
TI  - The convergence of Euler's broken lines
JO  - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY  - 2008
SP  - 163
EP  - 164
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VUU_2008_2_a52/
LA  - ru
ID  - VUU_2008_2_a52
ER  - 
%0 Journal Article
%A D. V. Khlopin
%T The convergence of Euler's broken lines
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2008
%P 163-164
%N 2
%U http://geodesic.mathdoc.fr/item/VUU_2008_2_a52/
%G ru
%F VUU_2008_2_a52
D. V. Khlopin. The convergence of Euler's broken lines. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 2 (2008), pp. 163-164. http://geodesic.mathdoc.fr/item/VUU_2008_2_a52/

[1] Khartman F., Obyknovennye differentsialnye uravneniya, Mir, M., 1970

[2] Mirica S., “Feedback differential systems: approximate and limitink trajectories”, Studia Univ. Babe s-Bolyai Math., 49:3 (2004), 83–96 | Zbl

[3] Khlopin D. V., “Lomanye Eilera v sistemakh s usloviyami Karateodori”, Trudy IMM UrO RAN, 13, no. 2, Ekaterinburg, 2007, 167–183