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Polynomial differential equations with small coefficients
Classes of polynomial non-autonomous differential equations of degree $n$ are considered. An explicit bound on the size
of the coefficients is given which implies that each equation in the class has exactly $n$ complex
periodic solutions. In most of the classes the upper bound can be improved when we consider
real periodic solutions.
We present a proof to a recent conjecture about the number of periodic solutions.
The results are used to give upper bounds for the number of limit cycles of polynomial two-dimensional systems.