9 research outputs found
Some Applications of the Extended Bendixson-Dulac Theorem
During the last years the authors have studied the number of limit cycles of
several families of planar vector fields. The common tool has been the use of
an extended version of the celebrated Bendixson-Dulac Theorem. The aim of this
work is to present an unified approach of some of these results, together with
their corresponding proofs. We also provide several applications.Comment: 19 pages, 3 figure
Renormalization group and isochronous oscillations
We show how the condition of isochronicity can be studied for two dimensional
systems in the renormalization group (RG) context. We find a necessary
condition for the isochronicity of the Cherkas and another class of cubic
systems. Our conditions are satisfied by all the cases studied recently by
Bardet et al \cite{bard} and Ghose Choudhury and Guh