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Bifurcation of the separatrix skeleton in some 1-parameter families of planar vector fields
Caubergh, Magdalena

Data: 2015
Resum: This article deals with the bifurcation of polycycles and limit cycles within the 1-parameter families of planar vector fields X_m^k, defined by =y^3-x^2k 1,=-x my^4k 1, where m is a real parameter and k1 integer. The bifurcation diagram for the separatrix skeleton of X_m^k in function of m is determined and the one for the global phase portraits of (X^1_m)_mR is completed. Furthermore for arbitrary k1 some bifurcation and finiteness problems of periodic orbits are solved. Among others, the number of periodic orbits of X_m^k is found to be uniformly bounded independent of mR and the Hilbert number for (X_m^k)_mR, that thus is finite, is found to be at least one.
Drets: Tots els drets reservats.
Llengua: Anglès
Document: article ; recerca ; preprint
Matèria: global phase portrait ; Hilbert’s 16th Problem ; Limit cycles ; nilpotent center problem ; rotated vector field ; separatrix skeleton
Publicat a: Journal of Differential Equations, Vol. 259 (2015) , p. 989-1013

DOI: 10.1016/j.jde.2015.02.036

28 p, 932.5 KB

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Documents de recerca > Documents dels grups de recerca de la UAB > Centres i grups de recerca (producció científica) > Ciències > GSD (Grup de sistemes dinàmics)
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