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Upper bounds for the number of zeroes for some Abelian integrals

Autor
Gasull, A.; Lazaro, J. Tomás; Torregrosa, J.
Tipus d'activitat
Article en revista
Revista
Nonlinear analysis, theory, methods and applications
Data de publicació
2012-09
Volum
75
Número
13
Pàgina inicial
5169
Pàgina final
5179
DOI
https://doi.org/10.1016/j.na.2012.04.033 Obrir en finestra nova
Repositori
http://hdl.handle.net/2117/16667 Obrir en finestra nova
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 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 bifurcat...
Citació
Gasull, A.; Lázaro, J.T.; Torregrosa, J. Upper bounds for the number of zeroes for some Abelian integrals. "Nonlinear analysis, theory, methods and applications", Setembre 2012, vol. 75, núm. 13, p. 5169-5179.
Paraules clau
Abelian integrals, Chebyshev system, Limit cycles, Number of zeroes of real functions, Weak 16th Hilbert's Problem
Grup de recerca
SD - Sistemes Dinàmics de la UPC

Participants