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Global phase portraits of some reversible cubic centers with noncollinear singularities
Caubergh, Magdalena (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Torregrosa Arús, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Data: 2013
Resum: The results in this paper show that the cubic vector fields ˙x = −y + M(x, y) − y(x2 + y2), y˙ = x + N(x, y) + x(x2 + y2), where M, N are quadratic homogeneous polynomials, having simultaneously a center at the origin and at infinity, have at least 61 and at most 68 topologically different phase portraits. To this end the reversible subfamily defined by M(x, y) = −γxy, N(x, y) = (γ − λ)x2 + α2λy2 with α, γ ∈ R and λ 6= 0, is studied in detail and it is shown to have at least 48 and at most 55 topologically different phase portraits. In particular, there are exactly 5 for γλ < 0 and at least 46 for γλ > 0. Furthermore, the global bifurcation diagram is analyzed.
Drets: Tots els drets reservats.
Llengua: Anglès
Document: article ; recerca ; preprint
Matèria: Reversible planar vector fields ; Cubic vector fields ; Global classification of phase portraits ; Bifurcation diagram
Publicat a: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, Vol. 23 Núm. 9 (2013) , p. 1350161 (30 pages), ISSN 1793-6551

DOI: 10.1142/S0218127413501617


38 p, 3.6 MB

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