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Pàgina inicial > Articles > Articles publicats > Upper bounds for the number of zeroes for some Abelian integrals |
Data: | 2012 |
Resum: | Consider the vector field x' = −yG(x, y), y' = xG(x, y), where the set of critical points {G(x, y) = 0} is formed by K straight lines, not passing through the origin and parallel to one or two orthogonal directions. We perturb it with a general polynomial perturbation of degree n and study which is the maximum number of limit cycles that can bifurcate from the period annulus of the origin in terms of K and n. Our approach is based on the explicit computation of the Abelian integral that controls the bifurcation and in a new result for bounding the number of zeroes of a certain family of real functions. When we apply our results for K ≤ 4 we recover or improve some results obtained in several previous works. |
Ajuts: | Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-410 Ministerio de Ciencia e Innovación MTM2009-06973 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-859 |
Drets: | Tots els drets reservats. |
Llengua: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Matèria: | Abelian integrals ; Weak 16th Hilbert's Problem ; Limit cycles ; Chebyshev system ; Number of zeroes of real functions |
Publicat a: | Nonlinear Analysis : Theory, Methods and Applications, Vol. 75 (2012) , p. 5169-5179, ISSN 0362-546X |
Postprint 15 p, 386.1 KB |