TY - JOUR

T1 - The algebraic curves of planar polynomial differential systems with homogeneous nonlinearities

AU - Cheresiz, Vladimir M.

AU - Volokitin, Evgenii P.

N1 - Funding Information: V. M. Cheresiz carried out research within the framework of the state contract of Sobolev Institute of Mathematics (project no. 0314-2019-0010). E. P. Volokitin carried out research within the framework of the state contract of Sobolev Institute of Mathematics (project no. 0314-2019-0007). Publisher Copyright: © 2021, University of Szeged. All rights reserved.

PY - 2021

Y1 - 2021

N2 - We consider planar polynomial systems of ordinary differential equations of the form ẋ=x+Pn (x, y), ẏ=y+Qn (x, y), where Pn (x, y), Qn (x, y) are homogeneous polynomials of degree n. We study the algebraic and non-algebraic invariant curves of these systems with emphasis on limit cycles.

AB - We consider planar polynomial systems of ordinary differential equations of the form ẋ=x+Pn (x, y), ẏ=y+Qn (x, y), where Pn (x, y), Qn (x, y) are homogeneous polynomials of degree n. We study the algebraic and non-algebraic invariant curves of these systems with emphasis on limit cycles.

KW - Algebraic limit cycles

KW - Polynomial systems

UR - http://www.scopus.com/inward/record.url?scp=85112318986&partnerID=8YFLogxK

U2 - 10.14232/EJQTDE.2021.1.51

DO - 10.14232/EJQTDE.2021.1.51

M3 - Article

AN - SCOPUS:85112318986

VL - 2021

JO - Electronic Journal of Qualitative Theory of Differential Equations

JF - Electronic Journal of Qualitative Theory of Differential Equations

SN - 1417-3875

M1 - 51

ER -