, Volume 4, Issue 4, pp 539-581

Countable Set of Limit Cycles for the Equation \(\frac{{dw}}{{dz}} = \frac{{P_n \left( {z,w} \right)}}{{Q_n \left( {z,w} \right)}}\)

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Abstract

Differential equations on the complex plane with a rational right-hand side are considered. In a generic case such equation has a countable set of homologically independent limit cycles. It is proved that the exceptional set – the set of equations such that they do not have this property – has the real codimension at least two in the space of equations with right-hand side of degree no greater than a fixed number n.