This research demonstrates increased limit cycles in perturbed hyperbolic polycycles with saddles, suggesting complex dynamics.
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.
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Andrei Valerevich Dukov (2025) studied this question.
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