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

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

2004-04-29

arxiv.org/abs/math/0404531v1

Mathematics

Dynamical Systems

58 pages, 2 Postscript figures, Latex

Scientific paper

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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