An example of eqations $\frac{dw}{dz}=\frac{P_n(z,w)}{Q_n(z,w)}$ having a countable number of limit cycles and arbitrarily large Petrovskii–Landis genus

In this work we construct an open set $V$ in the space of coefficients $A_n$ of the equations $\frac{dw}{dz}=\frac{P_n(z,w)}{Q_n(z,w)}$ such that on the solutions of an arbitrary equation $\alpha\in V$ there exist a countable number of homotopically distinct limit cycles. Also, for each natural number $N$ we construct an open set $V_N\subset A_n$ such that an arbitrary equation $\alpha\in V_N$ has a Petrovskii–Landis genus which exceeds $N$.
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