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On a class of invariant algebraic curves for Kukles systems. (English) Zbl 1389.34128

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.

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
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