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Página principal > Artículos > Artículos publicados > On the number of limit cycles for perturbed pendulum equations |
Fecha: | 2016 |
Resumen: | We consider perturbed pendulum-like equations on the cylinder of the form x (x)= _=0^mQ_n, (x) x^ where Q_n, are trigonometric polynomials of degree n, and study the number of limit cycles that bifurcate from the periodic orbits of the unperturbed case =0 in terms of m and n. Our first result gives upper bounds on the number of zeros of its associated first order Melnikov function, in both the oscillatory and the rotary regions. These upper bounds are obtained expressing the corresponding Abelian integrals in terms of polynomials and the complete elliptic functions of first and second kind. Some further results give sharp bounds on the number of zeros of these integrals by identifying subfamilies which are shown to be Chebyshev systems. |
Ayudas: | Ministerio de Economía y Competitividad MTM2013-40998-P Ministerio de Economía y Competitividad MTM2014-52209-C2-1-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 |
Nota: | Agraïments: The second author is supported by the project J3452 "Dynamical Systems Methods in Hydrodynamics" of the Austrian Science Fund (FWF). |
Derechos: | Tots els drets reservats. |
Lengua: | Anglès |
Documento: | Article ; recerca ; Versió acceptada per publicar |
Materia: | Abelian integrals ; Infinitesimal Sixteenth Hilbert problem ; Limit cycles ; Perturbed pendulum equation |
Publicado en: | Journal of differential equations, Vol. 261 Núm. 3 (2016) , p. 2141-2167, ISSN 1090-2732 |
Postprint 28 p, 402.2 KB |