E. P. Volokitin, V. M. Cheresiz, “Dynamics of the cubic Darboux systems”, Sib. Èlektron. Mat. Izv., 2017, Volume 14,Pages <nobr>889

This article is cited in 2 papers

Differentical equations, dynamical systems and optimal control

Dynamics of the cubic Darboux systems

E. P. Volokitin^ab, V. M. Cheresiz^a

^a Sobolev Institute of Mathematics, 4 Acad. Koptyug avenue, 630090 Novosibirsk Russia
^b Novosibirsk State University, 2 Pirogova Str., 630090 Novosibirsk Russia

Abstract: We study the local and global behavior of the trajectories of the differential systems of the form $\dot x= x+p_3(x,y), \ \dot y=y+q_3(x,y)$ where $p_3(x,y), q_3(x,y)$ are relatively prime homogeneous cubic polynomials.

Keywords: polynomial systems, singular points, Poincaré equator, phase portraits.

UDC: 514.7

MSC: 34С05

Received July 7, 2017, published September 14, 2017

DOI: 10.17377/semi.2017.14.075