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Planar cubic polynomial differential systems with the maximum number of invariant straight lines

Jaume Llibre·Nicolae Vulpe
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Abstract

We classify all cubic systems possessing the maximum number of invariant straight lines (real or complex) taking into account their multiplicities. We prove that there are exactly 23 topological different classes of such systems. For every class we provide the configuration of its invariant straight lines in the Poincare disc. Moreover, every class is characterized by a set of affine invariant conditions.

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Jaume Llibre, Nicolae Vulpe. 2004-04-29. Planar cubic polynomial differential systems with the maximum number of invariant straight lines. https://arxiv.org/abs/math/0404531

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