Stability Analysis of Critical Points in QuadraticSystems in R^{3} Which Contain a Plane of Critical Points
Abstract
Markus idea [ L. Markus, Quadratic Differential Equations and Nonassociative Algebras, Ann. Math. Studies 45 (Princeton Univ. Press, 1960), p. 185 ] of treating the quadratic systems of ODEs via commutative algebras which was introduced in 1960 is used in this paper to consider the stability of the origin. In [ M. Mencinger, submitted to Communications in Algebra ] all threedimensional commutative algebras which contain a twodimensional nil subalgebra were classified up to the algebraic isomorphism. This classification is used here to study the stability of the origin in the systems in R^{3} with a plane of critical points.
 Publication:

Progress of Theoretical Physics Supplement
 Pub Date:
 2003
 DOI:
 10.1143/PTPS.150.388
 Bibcode:
 2003PThPS.150..388M