Planar quadratic vector fields with invariant lines of total multiplicity at least five
Copyright policy )Planar quadratic vector fields with invariant lines of total multiplicity at least five
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.
50 pages, 4 Postscript figures, Latex
- Moldova State University, Institute of Mathematics and Computer Science Moldova (Republic of)
- Moldova State University Moldova (Republic of)
- University of Montreal Canada
- Academy of Sciences of Moldova Moldova (Republic of)
- Information Society Development Institute Moldova (Republic of)
Algebraic affine invariant, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, 13A50, Dynamical Systems (math.DS), 34C05, quadratic system, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), invariant line, quadratic differential system, algebraic invariant curve, configuration of invariant lines, FOS: Mathematics, Mathematics - Dynamical Systems, Symmetries, invariants of ordinary differential equations, 34C05; 13A50, Poincare compactification
Algebraic affine invariant, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, 13A50, Dynamical Systems (math.DS), 34C05, quadratic system, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), invariant line, quadratic differential system, algebraic invariant curve, configuration of invariant lines, FOS: Mathematics, Mathematics - Dynamical Systems, Symmetries, invariants of ordinary differential equations, 34C05; 13A50, Poincare compactification
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