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linking to equilibria at infinity in a cubic system
On the number of limit cycles of a cubic Near-Hamiltonian system
For the near-Hamiltonian system $\dot{x}=y+\varepsilon
P(x,y),\dot{y}=x-x^2+\varepsilon Q(x,y)$, where $P$ and $Q$ are
polynomials of $x,y$ having degree 3 with varying coefficients we
obtain 5 limit cycles.