Structural stability of planar quasi-homogeneous vector fields

• Published in: Journal of mathematical analysis and applications Vol. 468; no. 1; pp. 212 - 226
• Main Authors: Algaba, A., Fuentes, N., Gamero, E., Garcia, C.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.12.2018
• Subjects: Conservative–dissipative splitting; Quasi-homogeneous vector fields; Structural stability; Structural stability; Conservative–dissipative splitting; Quasi-homogeneous vector fields
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2018.08.005

In this work, we study the structural stability of planar quasi-homogeneous vector fields under quasi-homogeneous perturbations, and provide a complete classification. This study, which has been the subject of previous works, is only complete in the homogeneous case. The main tool in our analysis is a splitting of planar quasi-homogeneous vector fields into conservative–dissipative parts. Moreover, we describe the topological equivalence classes in the set of the structurally stable planar quasi-homogeneous vector fields. Finally, we include some examples where the equivalence classes are determined.