Lower bound for the cyclicity of hyperbolic polycycles

Consider a monodromic hyperbolic polycycle formed by $n$ saddles and $n$ separatrix connections. Let the product of the characteristic numbers of these saddles be equal to 1. It is shown that for any positive integer $n$, in a perturbation of this polycycle in a generic $(n+1)$-parameter family at least $n+1$ limit cycles appear. Bibliography: 26 titles.