Geodesic
Local Finitely Smooth Equivalence of Real Autonomous Systems with Two Pure Imaginary Eigenvalues
Matematičeskie zametki, Tome 92 (2012) no. 6, pp. 912-927.

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

The paper deals with real autonomous systems of ordinary differential equations in a neighborhood of a nondegenerate singular point such that the matrix of the linearized system has two pure imaginary eigenvalues, all other eigenvalues lying outside the imaginary axis. It is proved that, for such systems having a focus on the center manifold, the problem of finitely smooth equivalence is solved in terms of the finite segments of the Taylor series of their right-hand sides.
Keywords: autonomous system of ordinary differential equations, finitely smooth equivalence of systems, pseudonormal form, resonance, shearing transformation. 
@article{MZM_2012_92_6_a11,
     author = {V. S. Samovol},
     title = {Local {Finitely} {Smooth} {Equivalence} of {Real} {Autonomous} {Systems} with {Two} {Pure} {Imaginary} {Eigenvalues}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {912--927},
     publisher = {mathdoc},
     volume = {92},
     number = {6},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_92_6_a11/}
}
TY  - JOUR
AU  - V. S. Samovol
TI  - Local Finitely Smooth Equivalence of Real Autonomous Systems with Two Pure Imaginary Eigenvalues
JO  - Matematičeskie zametki
PY  - 2012
SP  - 912
EP  - 927
VL  - 92
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2012_92_6_a11/
LA  - ru
ID  - MZM_2012_92_6_a11
ER  - 
%0 Journal Article
%A V. S. Samovol
%T Local Finitely Smooth Equivalence of Real Autonomous Systems with Two Pure Imaginary Eigenvalues
%J Matematičeskie zametki
%D 2012
%P 912-927
%V 92
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2012_92_6_a11/
%G ru
%F MZM_2012_92_6_a11
V. S. Samovol. Local Finitely Smooth Equivalence of Real Autonomous Systems with Two Pure Imaginary Eigenvalues. Matematičeskie zametki, Tome 92 (2012) no. 6, pp. 912-927. http://geodesic.mathdoc.fr/item/MZM_2012_92_6_a11/

[1] V. S. Samovol, “O novykh rezonansakh i normalnoi forme avtonomnykh sistem s odnim nulevym kornem”, Matem. zametki, 88:1 (2010), 63–77 | DOI | MR | Zbl

[2] V. S. Samovol, “Konechno-gladkaya lokalnaya ekvivalentnost avtonomnykh sistem s odnim nulevym kornem”, Matem. zametki, 88:2 (2010), 275–287 | DOI | MR

[3] V. S. Samovol, “O psevdonormalnoi forme veschestvennykh avtonomnykh sistem s dvumya chisto mnimymi sobstvennymi chislami”, Matem. zametki, 92:5, 731–746 | DOI

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

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

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

[7] 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

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

[9] V. S. Samovol, “Konechno-gladkaya normalnaya forma avtonomnoi sistemy s dvumya chisto mnimymi kornyami”, Matem. zametki, 80:2 (2006), 270–281 | DOI | MR | Zbl

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

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