Qualitative Planar Dynamics with Star Nodes and Homogeneous Nonlinearities: Beyond Hilbert’s 16th Problem
Abstract
Abstract This is a full study of the dynamics of polynomial planar vector fields whose linear part is a multiple of the identity and whose nonlinear part is a homogeneous polynomial of arbitrary degree $$n>1$$ . It extends previous work by other authors that was mainly concerned with the existence and number of limit cycles. The general results are also applied to two classes of examples where the nonlinearities have degrees 2 and 3, for which we provide a set of phase portraits.
Fields of Study & Subjects
Advanced Differential Equations and Dynamical Systems
Quantum chaos and dynamical systems
Mathematical Dynamics and Fractals
Publication details
- Journal / source
- Matemática Contemporânea
- Publisher
- Springer Science and Business Media LLC
- Publication date
- 22 July 2026
- Language
- EN