Bifurcation of limit cycles from some uniform isochronous centers
This article concerns with the weak 16-th Hilbert problem. More precisely, we consider the uniform isochronous centers x'=-y x^(n-1) y, y'= x x^(n-2) y^2 , for n = 2, 3, 4, and we perturb them by all homogeneous polynomial of degree 2, 3, 4, respectively. Using averaging theory of first or...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:145277 |
| Acceso en línea: | https://ddd.uab.cat/record/145277 |
| Access Level: | acceso abierto |
| Palabra clave: | Averaging theory Periodic solutions Uniform isochronous centers Weak Hilbert problem |
| Sumario: | This article concerns with the weak 16-th Hilbert problem. More precisely, we consider the uniform isochronous centers x'=-y x^(n-1) y, y'= x x^(n-2) y^2 , for n = 2, 3, 4, and we perturb them by all homogeneous polynomial of degree 2, 3, 4, respectively. Using averaging theory of first order we prove that the maximum number N (n) of limit cycles that can bifurcate from the periodic orbits of the centers for n = 2, 3, under the mentioned perturbations, is 2. We prove that N (4) 2, but there is numerical evidence that N (4) = 2. Finally we conjecture that using averaging theory of first order N (n) = 2 for all n. |
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