Geodesic
Existence of a right system whose upper-limit central and general indexes do not coincide with lower-limit ones
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2019), pp. 53-57 
V. I. Kokushkin. Existence of a right system whose upper-limit central and general indexes do not coincide with lower-limit ones. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2019), pp. 53-57. http://geodesic.mathdoc.fr/item/VMUMM_2019_2_a10/
@article{VMUMM_2019_2_a10,
     author = {V. I. Kokushkin},
     title = {Existence of a right system whose upper-limit central and general indexes do not coincide with lower-limit ones},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {53--57},
     year = {2019},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2019_2_a10/}
}
TY  - JOUR
AU  - V. I. Kokushkin
TI  - Existence of a right system whose upper-limit central and general indexes do not coincide with lower-limit ones
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2019
SP  - 53
EP  - 57
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2019_2_a10/
LA  - ru
ID  - VMUMM_2019_2_a10
ER  - 
%0 Journal Article
%A V. I. Kokushkin
%T Existence of a right system whose upper-limit central and general indexes do not coincide with lower-limit ones
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2019
%P 53-57
%N 2
%U http://geodesic.mathdoc.fr/item/VMUMM_2019_2_a10/
%G ru
%F VMUMM_2019_2_a10

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

On the one hand, we show that the upper-limit analogues of Vinograd–Millionschikov central exponents determined on the space of regular linear differential systems are equal to lower-limit ones. A similar fact is also valid for analogues of Bohl–Persidsky general exponents on the space of almost reducible systems. On the other hand, we present an example of a two-dimensional regular differential system with piecewise continuous bounded coefficients having noncoinciding upper-limit and lower-limit central and general exponents.

[1] Bylov B. F., Vinograd R. E., Grobman D. M., Nemytskii V. V., Teoriya pokazatelei Lyapunova i ee prilozheniya k voprosam ustoichivosti, Nauka, M., 1966 | MR

[2] Vinograd R. E., “O tsentralnom kharakteristicheskom pokazatele sistemy differentsialnykh uravnenii”, Matem. sb., 42:2 (1957), 207–222 | Zbl

[3] Millionschikov V. M., “Dokazatelstvo dostizhimosti tsentralnykh pokazatelei”, Sib. matem. zhurn., 10:1 (1969), 99–104 | MR

[4] Izobov N. A., “O mnozhestve nizhnikh pokazatelei lineinoi differentsialnoi sistemy”, Differents. uravneniya, 1:4 (1965), 469–477 | MR | Zbl

[5] Bohl P., “Uber Differentialungleichungen”, J. reine und angew. Math., 144:4 (1913), 284–318 | MR

[6] Persidskii K. P., “K teorii ustoichivosti integralov sistemy differentsialnykh uravnenii. Chast 1”, Izv. fiz.-mat. o-va pri Kazan. un-te. Ser. 3, VIII, 47–85 | MR

[7] Vinograd R. E., “Simultaneous attainability of central Lyapunov and Bohl exponents for ODE linear systems”, Proc. Amer. Math. Soc., 88:4 (1983), 595–601 | DOI | MR | Zbl

[8] Barabanov E. A., Konyukh A. V., “Bohl exponents of linear differential systems”, Mem. Diff. Eq. and Math. Phys., 24 (2001), 151–158 | MR | Zbl

[9] Bylov B. F., “Pochti privodimye sistemy”, Sib. matem. zhurn., 3:3 (1962), 333–359 | MR | Zbl

[10] Cergeev I. N., “Nekotorye svoistva tsentralnykh pokazatelei lineinykh differentsialnykh sistem”, XVII Mezhdunar. nauchn. konf. po differents. uravneniyam (Eruginskie chteniya — 2017), Tez. dokl. Minsk, 16–20 maya 2017 g., v. 1, In-t matem. NAN Belarusi, Minsk, 2017, 36–37