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Upper bounds for the number of zeroes for some Abelian integrals
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

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.
Drets: Tots els drets reservats.
Llengua: Anglès
Document: article ; recerca ; preprint
Matèria: Abelian integrals ; Weak 16th Hilbert’s Problem ; Limit cycles ; Chebyshev system ; Number of zeroes of real functions
Publicat a: Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods, Vol. 75 (2012) , p. 5169-5179, ISSN 0362-546X

DOI: 10.1016/

15 p, 386.1 KB

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