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SM ISO690:2012 SCHLOMIUK, Dana, VULPE, Nicolae. Planar quadratic vector fields with invariant lines of total multiplicity at least five. In: Qualitative Theory of Dynamical Systems, 2004, vol. 5, pp. 135-194. ISSN 1575-5460. DOI: https://doi.org/10.1007/BF02968134 |
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Qualitative Theory of Dynamical Systems | ||||||
Volumul 5 / 2004 / ISSN 1575-5460 /ISSNe 1662-3592 | ||||||
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DOI:https://doi.org/10.1007/BF02968134 | ||||||
Pag. 135-194 | ||||||
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In this article we consider the action of the real affine group and time rescaling on real 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 real 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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Cuvinte-cheie Algebraic affine invariant, algebraic invariant curve, configuration of invariant lines, Poincare compactification, quadratic differential system |
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