Per citar aquest document: http://ddd.uab.cat/record/150598
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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, 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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