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Pàgina inicial > Articles > Articles publicats > Limit cycles appearing from the perturbation of a system with a multiple line of critical points |
Data: | 2012 |
Resum: | Consider the planar ordinary differential equation ˙x = −y(1 − y)m, y˙ = x(1 − y)m, where m is a positive integer number. We study the maximum number of zeroes of the Abelian integral M that controls the limit cycles that bifurcate from the period annulus of the origin when we perturb it with an arbitrary polynomial vector field. One of the key points of our approach is that we obtain a simple expression of M based on some successive reductions of the integrals appearing during the procedure. |
Ajuts: | Ministerio de Ciencia e Innovación MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 |
Nota: | Agraïments: The second author is partially supported by NSFC-10831003 and by AGAUR grant number 2009PIV00064. |
Drets: | Tots els drets reservats. |
Llengua: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Matèria: | Limit cycles ; Weak Hilbert's 16th Problem ; Abelian integrals ; Bifurcation of periodic orbits |
Publicat a: | Nonlinear Analysis : Theory, Methods and Applications, Vol. 75 (2012) , p. 278-285, ISSN 0362-546X |
Postprint 11 p, 279.4 KB |