On a class of invariant algebraic curves for Kukles systems

Abstract

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.

Keywords

• kukles system
• invariant curve
• integrability
• limit cycle