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The Center Variety of Polynomial Differential Systems

Abdul Salam Jarrah·Reinhard Laubenbacher·Valery Romanovski
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Abstract

We investigate the symmetry component of the center variety of polynomial differential systems, corresponding to systems with an axis of symmetry in the real plane. We give a general algorithm to find this irreducible subvariety and compute its dimension. We show that our methods provide a simple way to compute the radical of the ideal generated by the focus quantities and, therefore, to estimate the cyclicity of a center in the case when the ideal is radical. In particular, we use our methods to get a simple proof of the famous Bautin theorem on the cyclicity of the quadratic system.

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Abdul Salam Jarrah, Reinhard Laubenbacher, Valery Romanovski. 2001-12-20. The Center Variety of Polynomial Differential Systems. https://arxiv.org/abs/math/0009061

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