Geodesic
Finitely Smooth Normal Form of an Autonomous System with Two Pure Imaginary Roots
Matematičeskie zametki, Tome 80 (2006) no. 2, pp. 270-281

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

We consider the problem of finitely smooth normalization of a system of ordinary differential equations whose linear part has two eigenvalues, while the other eigenvalues lie outside the imaginary axis.
Keywords: autonomous system of ODE, normal form, singular point, weakly degenerate system, finitely smooth equivalence. 
V. S. Samovol. Finitely Smooth Normal Form of an Autonomous System with Two Pure Imaginary Roots. Matematičeskie zametki, Tome 80 (2006) no. 2, pp. 270-281. http://geodesic.mathdoc.fr/item/MZM_2006_80_2_a12/
@article{MZM_2006_80_2_a12,
     author = {V. S. Samovol},
     title = {Finitely {Smooth} {Normal} {Form} of an {Autonomous} {System} with {Two} {Pure} {Imaginary} {Roots}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {270--281},
     year = {2006},
     volume = {80},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_80_2_a12/}
}
TY  - JOUR
AU  - V. S. Samovol
TI  - Finitely Smooth Normal Form of an Autonomous System with Two Pure Imaginary Roots
JO  - Matematičeskie zametki
PY  - 2006
SP  - 270
EP  - 281
VL  - 80
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/MZM_2006_80_2_a12/
LA  - ru
ID  - MZM_2006_80_2_a12
ER  - 
%0 Journal Article
%A V. S. Samovol
%T Finitely Smooth Normal Form of an Autonomous System with Two Pure Imaginary Roots
%J Matematičeskie zametki
%D 2006
%P 270-281
%V 80
%N 2
%U http://geodesic.mathdoc.fr/item/MZM_2006_80_2_a12/
%G ru
%F MZM_2006_80_2_a12

[1] V. S. Samovol, “Normalnaya forma avtonomnoi sistemy s odnim nulevym kornem”, Matem. zametki, 75:5 (2004), 711–720 | MR | Zbl

[2] A. D. Bryuno, Lokalnyi metod nelineinogo analiza differentsialnykh uravnenii, Nauka, M., 1979 | MR

[3] A. D. Bryuno, “Analiticheskaya forma differentsialnykh uravnenii”, Tr. MMO, 25, 1971, 119–262 | MR | Zbl

[4] V. S. Samovol, “Ekvivalentnost sistem differentsialnykh uravnenii v okrestnosti osoboi tochki”, Tr. MMO, 44, 1982, 213–234 | MR | Zbl

[5] G. R. Belitskii, “Gladkaya ekvivalentnost rostkov vektornykh polei”, Funktsion. analiz i ego prilozh., 20:4 (1986), 1–8 | MR

[6] A. N. Kuznetsov, “Differentsiruemye resheniya vyrozhdayuschikhsya sistem obyknovennykh uravnenii”, Funktsion. analiz i ego prilozh., 6:2 (1972), 41–51 | MR | Zbl

[7] A. D. Bryuno, V. Yu. Petrovich, Normalnye formy sistemy ODU, Preprint Instituta prikladnoi matematiki im. M. V. Keldysha RAN No 18, 2000

[8] V. S. Samovol, “O neobkhodimom i dostatochnom uslovii gladkoi linearizatsii avtonomnoi sistemy na ploskosti v okrestnosti osoboi tochki”, Matem. zametki, 46:1 (1989), 67–77 | MR | Zbl