Uniqueness of the limit cycles for complex differential equations with two monomials

We prove that any complex differential equation with two monomials of the form z ˙ = a k ¯ l + b m n , non-negative integers and ∈ C has one limit cycle at most. Moreover, we characterise when such exists then it is hyperbolic. For an arbitrary above form, also solve centre-focus problem examine number, position, type its critical points. In particular, Berlinskiĭ-type result regarding geometrical distribution points stabilities.