Osuna, Osvaldo; Rebollo-Perdomo, Salomón; Villasenor-Aguilar, Gabriel On a class of invariant algebraic curves for Kukles systems. (English) Zbl 1389.34128 Electron. J. Qual. Theory Differ. Equ. 2016, Paper No. 61, 12 p. (2016). Summary: In this paper we give a new upper bound for the degree of a class of transversal to infinity invariant algebraic curves for polynomial Kukles systems of arbitrary degree. Moreover, we prove that a quadratic Kukles system having at least one transversal to infinity invariant algebraic curve is integrable. Cited in 1 Document MSC: 34C45 Invariant manifolds for ordinary differential equations 34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations 34C14 Symmetries, invariants of ordinary differential equations 34A05 Explicit solutions, first integrals of ordinary differential equations Keywords:Kukles system; invariant curve; integrability; limit cycle PDFBibTeX XMLCite \textit{O. Osuna} et al., Electron. J. Qual. Theory Differ. Equ. 2016, Paper No. 61, 12 p. (2016; Zbl 1389.34128) Full Text: DOI