Planar quadratic vector fields with invariant lines of total multiplicity at least five

Details Planar quadratic vector fields with invariant lines of total multiplicity at least five Planar quadratic vector fields with invariant lines of total multiplicity at least five

2004-05-06

arxiv.org/abs/math/0405094v1

Mathematics

Dynamical Systems

50 pages, 4 Postscript figures, Latex

Scientific paper

In this article we consider the action of affine group and time rescaling on planar quadratic differential systems. We construct a system of representatives of the orbits of systems with at least five invariant lines, including the line at infinity and including multiplicities. For each orbit we exhibit its configuration. We characterize in terms of algebraic invariants and comitants and also geometrically, using divisors of the complex projective plane, the class of quadratic differential systems with at least five invariant lines. These conditions are such that no matter how a system may be presented, one can verify by using them whether the system has or does not have at least five invariant lines and to check to which orbit (or family of orbits) it belongs.

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