E. P. Volokitin, S. A. Treskov, V. M. Cheresiz, “Quadratic and сubic complex systems satisfying the Cauchy–Riemann conditions”, Sib. Èlektron. Mat. Izv., 2015, Volume 12,Pages <nobr>45

Differentical equations, dynamical systems and optimal control

Quadratic and сubic complex systems satisfying the Cauchy–Riemann conditions

E. P. Volokitin^ab, S. A. Treskov^ab, V. M. Cheresiz^a

^a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^b Novosibirsk State University

Abstract: We study plane quadratic and cubic differential systems satisfying the Cauсhy–Riemann conditions. We construct all global topologically equivalent phase portraits of the systems.

Keywords: quadratic systems, cubic systems, Darboux integrability, rational first integrals, phase portraits.

UDC: 517.925

MSC: 34С05

Received December 3, 2014, published January 25, 2015

DOI: 10.17377/semi.2015.12.005