# Dulac-Cherkas function in a neighborhood of a structurally unstable focus of an autonomous polynomial system on the plane

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The cubic function H(x, y) = xy2 + 2ey - x2 - (2 + e2 ) x - (1 + 2e2 ) = h is a Hamiltonian function of the following system: áº‹ = 2xy + 2e, áº = (2 + e2 ) + 2x - y2, which can be bifurcated out at least four limit cycles after a cubic polynomial disturbance, i.e., B(2, 3) â‰¥ 4.