Limit cycles coming from some uniform isochronous centers
This article is about the weak 16--th Hilbert problem, i.e. we analyze how many limit cycles can bifurcate from the periodic orbits of a given polynomial differential center when it is perturbed inside a class of polynomial differential systems. More precisely, we consider the uniform isochronous ce...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2016 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:169459 |
| Acceso en línea: | https://ddd.uab.cat/record/169459 https://dx.doi.org/urn:doi:10.1515/ans-2015-5010 |
| Access Level: | acceso abierto |
| Palabra clave: | Averaging theory Uniform isochronous centers Weak Hilbert problem |
| Sumario: | This article is about the weak 16--th Hilbert problem, i.e. we analyze how many limit cycles can bifurcate from the periodic orbits of a given polynomial differential center when it is perturbed inside a class of polynomial differential systems. More precisely, we consider the uniform isochronous centers \[ x= -y x^2 y (x^2 y^2)^n, y= x x y^2 (x^2 y^2)^n, \] of degree 2n 3 and we perturb them inside the class of all polynomial differential systems of degree 2n 3. For n=0,1 we provide the maximum number of limit cycles, 3 and 8 respectively, that can bifurcate from the periodic orbits of these centers using averaging theory of first order, or equivalently Abelian integrals. For n=2 we show that at least 12 limit cycles can bifurcate from the periodic orbits of the center. |
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