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The cyclicity of a cubic system with nonradical Bautin ideal |
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| Authors: | Viktor Levandovskyy |
| Affiliation: | a Lehrstuhl D für Mathematik, RWTH Aachen University, Templergraben 64, D-52062 Aachen, Germany b CAMTP - Center for Applied Mathematics and Theoretical Physics, University of Maribor, Krekova 2, SI-2000 Maribor, Slovenia c Mathematics Department, University of North Carolina at Charlotte, Charlotte, NC 28223, USA |
| Abstract: | We present a method for investigating the cyclicity of an elementary focus or center of a polynomial system of differential equations by means of complexification of the system and application of algorithms of computational algebra, showing an approach to treating the case that the Bautin ideal B of focus quantities is not a radical ideal (more precisely, when the ideal BK is not radical, where BK is the ideal generated by the shortest initial string of focus quantities that, like the Bautin ideal, determines the center variety). We illustrate the method with a family of cubic systems. |
| Keywords: | Bautin ideal Cyclicity Polynomial system |
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