Geodesic
Rotation number like total characteristic of stability of Hill equation
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 2 (2009), pp. 26-32 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Hill equation is considered. After transition to polar coordinates differential equation on torus for polar corner, satisfying to Karateodori conditions is gained. We shall give basic results. Hill equation (with various multiplicators) is strongly stable (strongly unstable) then and only then, when the rotation number is nonintegral (integral) nonnegative number. Formula connecting the nonintegral rotation number with multiplicators of Hill equation is received.
Keywords: strong stability, differential equations on torus, the number of rotation, multiplicators. 
@article{VSGU_2009_2_a2,
     author = {A. A. Zhukova},
     title = {Rotation number like total characteristic of stability of {Hill} equation},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {26--32},
     year = {2009},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2009_2_a2/}
}
TY  - JOUR
AU  - A. A. Zhukova
TI  - Rotation number like total characteristic of stability of Hill equation
JO  - Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
PY  - 2009
SP  - 26
EP  - 32
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VSGU_2009_2_a2/
LA  - ru
ID  - VSGU_2009_2_a2
ER  - 
%0 Journal Article
%A A. A. Zhukova
%T Rotation number like total characteristic of stability of Hill equation
%J Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
%D 2009
%P 26-32
%N 2
%U http://geodesic.mathdoc.fr/item/VSGU_2009_2_a2/
%G ru
%F VSGU_2009_2_a2
A. A. Zhukova. Rotation number like total characteristic of stability of Hill equation. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 2 (2009), pp. 26-32. http://geodesic.mathdoc.fr/item/VSGU_2009_2_a2/

[1] Yakubovich V. A., Starzhinskii V. M., Lineinye differentsialnye uravneniya s periodicheskimi koeffitsientami i ikh prilozheniya, Nauka, M., 1972 | MR

[2] Koddington E. A., Levinson N. M., Teoriya obyknovennykh differentsialnykh uravnenii, Iz-vo inostr. lit., M., 1958

[3] Pliss V. A., Nelokalnye problemy teorii kolebanii, Nauka, M.–L., 1964 | MR

[4] Chezari L., Asimptoticheskoe povedenie i ustoichivost reshenii obyknovennykh differentsialnykh uravnenii, Mir, M., 1964

[5] Khartman F., Obyknovennye differentsialnye uravneniya, Mir, M., 1970 | MR

[6] Zhukovskii N. E., “Usloviya konechnosti integralov uravneniya $d^2y/d^2x+py=0$”, Matem. sb., 16:3 (1892), 582-591