Limit cycles bifurcating from a degenerate center
We study the maximum number of limit cycles that can bifurcate from a degenerate center of a cubic homogeneous polynomial differential system. Using the averaging method of second order and perturbing inside the class of all cubic polynomial differential systems we prove that at most three limit cyc...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2016 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/81601 |
| Acceso en línea: | https://hdl.handle.net/2117/81601 https://dx.doi.org/10.1016/j.matcom.2015.05.005 |
| Access Level: | acceso abierto |
| Palabra clave: | Geometry, Differencial Polynomial differential systems Centers Limit cycles Averaging theory HILBERTS 16TH PROBLEM HAMILTONIAN CENTERS PERIODIC-ORBITS VECTOR-FIELDS SYSTEMS ORDER SHAPE Geometria diferencial Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Ordres, reticles, estructures algebraiques ordenades |
| Sumario: | We study the maximum number of limit cycles that can bifurcate from a degenerate center of a cubic homogeneous polynomial differential system. Using the averaging method of second order and perturbing inside the class of all cubic polynomial differential systems we prove that at most three limit cycles can bifurcate from the degenerate center. As far as we know this is the first time that a complete study up to second order in the small parameter of the perturbation is done for studying the limit cycles which bifurcate from the periodic orbits surrounding a degenerate center (a center whose linear part is identically zero) having neither a Hamiltonian first integral nor a rational one. This study needs many computations, which have been verified with the help of the algebraic manipulator Maple. |
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