Abstract

I will describe a method for investigating the cyclicity of an elementary focus or center of a polynomial system of differential equations on R2 by complexifying the system and applying algorithms of computational algebra, and show an approach to treating the case that the Bautin ideal B of focus quantities is not a radical ideal. (Actually, letting B_K denote the ideal generated by the shortest initial string of focus quantities that, like the Bautin ideal, determines the center variety, it is the ideal B_K that is not radical.) I will illustrate the method with a family of cubic systems.

Joint work with Viktor Levandovskyy and Valery Romanovski.