Darboux-type center conditions for families of planar polynomial vector fields
Abstract
We study the center-focus problem for planar polynomial vector fields, which can be viewed as a local version of Hilbert's 16th problem. Based on a Lyapunov function approach, we establish novel results regarding the center-focus conditions for two families of differential systems. More precisely, we find an enclosure of the Bautin ideal generated by the Lyapunov constants of these systems. Our results hold for any degree $n \geq 2$.
Fields of Study & Subjects
Advanced Differential Equations and Dynamical Systems
Mathematical Dynamics and Fractals
Control and Stability of Dynamical Systems
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 26 February 2026
- Language
- EN
- Document type
- Preprint