Geodesic
Finitely Smooth Local Equivalence of Autonomous Systems with One Zero Root
Matematičeskie zametki, Tome 88 (2010) no. 2, pp. 275-287.

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

In this paper, in a neighborhood of a singular point, we consider autonomous systems of ordinary differential equations such that the matrix of their linear part has one zero eigenvalue, while the other eigenvalues lie outside the imaginary axis. We prove that the problem of finitely smooth equivalence can be solved for such systems by using finite segments of the Taylor series of their right-hand sides.
Keywords: autonomous system, ordinary differential equations, finitely smooth equivalence, singular point, zero eigenvalue, Taylor series, normal form, $N$-jet of a function. 
@article{MZM_2010_88_2_a9,
     author = {V. S. Samovol},
     title = {Finitely {Smooth} {Local} {Equivalence} of {Autonomous} {Systems} with {One} {Zero} {Root}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {275--287},
     publisher = {mathdoc},
     volume = {88},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_88_2_a9/}
}
TY  - JOUR
AU  - V. S. Samovol
TI  - Finitely Smooth Local Equivalence of Autonomous Systems with One Zero Root
JO  - Matematičeskie zametki
PY  - 2010
SP  - 275
EP  - 287
VL  - 88
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2010_88_2_a9/
LA  - ru
ID  - MZM_2010_88_2_a9
ER  - 
%0 Journal Article
%A V. S. Samovol
%T Finitely Smooth Local Equivalence of Autonomous Systems with One Zero Root
%J Matematičeskie zametki
%D 2010
%P 275-287
%V 88
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2010_88_2_a9/
%G ru
%F MZM_2010_88_2_a9
V. S. Samovol. Finitely Smooth Local Equivalence of Autonomous Systems with One Zero Root. Matematičeskie zametki, Tome 88 (2010) no. 2, pp. 275-287. http://geodesic.mathdoc.fr/item/MZM_2010_88_2_a9/

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

[2] B. C. Samovol, “O novykh rezonansakh i normalnoi forme avtonomnoi sistemy s odnim nulevym kornem”, Matem. zametki, 88:1, 63–77

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

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

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

[6] G. R. Belitskii, “Gladkaya ekvivalentnost rostkov vektornykh polei s odnim nulevym ili paroi chisto mnimykh sobstvennykh znachenii”, Funkts. analiz i ego pril., 20:4 (1986), 1–8 | MR | Zbl

[7] V. Vazov, Asimptoticheskie razlozheniya reshenii obyknovennykh differentsialnykh uravnenii, Mir, M., 1968 | MR | Zbl