Abstract
In this paper, we study the complexity of integrability of planar polynomial differential systems whose eigenvalues admit resonances at a saddle singular point. We prove that for arbitrary integer n≥2, if one of n+2 and 2n+1 is a prime number, then there exists a polynomial differential system of degree n with 1:−2 resonance at its saddle singular point such that the saddle order can be as high as n2−1.
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