Simultaneous bifurcation of limit cycles from a linear center with extra singular points
The period annuli of the planar vector field x' = -yF(x, y), y' = xF(x, y), where the set {F(x, y) = 0} consists of k different isolated points, is defined by k + 1 concentric annuli. In this paper we perturb it with polynomials of degree n and we study how many limit cycles bifurcate, up...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2014 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:150709 |
| Acceso en línea: | https://ddd.uab.cat/record/150709 https://dx.doi.org/urn:doi:10.1016/j.bulsci.2013.09.004 |
| Access Level: | acceso abierto |
| Palabra clave: | Polynomial perturbation of centers Piecewise rational abelian integral Simultaneity of limit cycles from several period annuli |
| Sumario: | The period annuli of the planar vector field x' = -yF(x, y), y' = xF(x, y), where the set {F(x, y) = 0} consists of k different isolated points, is defined by k + 1 concentric annuli. In this paper we perturb it with polynomials of degree n and we study how many limit cycles bifurcate, up to a first order analysis, from all the period annuli simultaneously in terms of k and n. Additionally, we prove that the associated Abelian integral is piecewise rational and, when k = 1, the provided upper bound is reached. Finally, the case k = 2 is also treated. |
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