Geodesic
Unbounded solutions of the polynomial Cauchy--Riemann systems
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 494-507.

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

We study the behavior of the trajectories of the Cauchy–Riemann polynomial differential systems at infinity. We use our results to construct the phase portraits for some special cases.
Keywords: singular points at infinity, Poincaré equator, separarices, polynomial first integrals. 
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E. P. Volokitin. Unbounded solutions of the polynomial Cauchy--Riemann systems. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 494-507. http://geodesic.mathdoc.fr/item/SEMR_2014_11_a61/

[1] Gregor J., “Dynamické systémy s regulární pravou stranou, I”, Pokroky matematiky, fyziky a astronomie, 3:2 (1958), 153–160 | Zbl

[2] Gavrilov N. I., Metody teorii obyknovennykh differentsialnykh uravnenii, Vysshaya shkola, M., 1962 | MR | Zbl

[3] Lukashevich N. A., “Izokhronnost tsentra nekotorykh sistem differentsialnykh uravnenii”, Differentsialnye uravneniya, 1:5 (1965), 295–302 | MR

[4] Pleshkan I. I., “Novyi sposob issledovaniya na izokhronnost sistemy dvukh differentsialnykh uravnenii”, Differentsialnye uravneniya, 5:6 (1969), 1083–1090 | Zbl

[5] Villarini M., “Regularity propeties of the period function near a centre of planar vector fields”, Nonlinear Analysis, 19:8 (1992), 787–803 | DOI | MR | Zbl

[6] Mardešić P., Rousseau C., Toni B., “Linearization of isochronous centers”, Journal of Differential Equations, 121:1 (1995), 67–108 | DOI | MR | Zbl

[7] Christopher C. J., Devlin J., “Isochronous centers in planar polynomial systems”, SIAM J. Math. Anal., 28:1 (1997), 162–177 | DOI | MR | Zbl

[8] Volokitin E. P., Cheresiz V. M., “Osobye tochki i pervye integraly golomorfnykh dinamicheskikh sistem”, Vestnik NGU. Ser.: Matematika, mekhanika, informatika, 13:2 (2013), 21–37 | Zbl

[9] Volokitin E. P., “Integriruemost po Darbu polinomialnykh kompleksnykh sistem”, Sibirskie elektronnye matematicheskie izvestiya, 10 (2013), 271–284 | MR

[10] Sabatini M., “Characterizing isochronous centres by Lie brackets”, Differential Equations and Dynamical Systems, 5:1 (1997), 91–99 | MR | Zbl

[11] Arnold V. I., Matematicheskie metody klassicheskoi mekhaniki, Nauka, M., 1979 | MR | Zbl

[12] Rylov A. I., “Novye spiralnye i sloistye techeniya kak primery sopryazhennykh techenii neszhimaemoi zhidkosti”, Doklady RAN, 457:4 (2014)

[13] Gonzáles Velasco, Enrique A., “Generic propeties of polynomial vector fields at infinity”, Trans. Amer. Math. Soc., 143 (1969), 201–222 | DOI | MR | Zbl

[14] Bautin N. N., Leontovich E. A., Metody i priemy kachestvennogo issledovaniya dinamicheskikh sistem na ploskosti, Nauka, M., 1990 | MR | Zbl

[15] Andronov A. A. i dr., Kachestvennaya teoriya dinamicheskikh sistem na ploskosti, Nauka, M., 1966 | MR | Zbl

[16] Conti R., “Centers of planar polynomial systems: A review”, Le Mathematiche, LIII:II (1998), 207–240 | MR | Zbl