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Algebraic and topological classification of the homogeneous cubic vector fields in the plane. (English) Zbl 0711.34061
By using the classification of fourth order binary forms in the real domain, an algebraic classification of systems \(x'=P(x,y)\), \(y'=Q(x,y)\), P, Q homogeneous polynomials of degree 3 is obtained. After a study of phase portraits for the general case when P and Q have the same degree and no common factor, all possible phase portraits are obtained for degree three.
Reviewer: A.Halanay

37G05 Normal forms for dynamical systems
Full Text: DOI
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