Structural Stability of Planar Homogeneous Polynomial Vector Fields: Applications to Critical Points and to Infinity
✍ Scribed by Jaume Llibre; Jesús S. Pérez del Rı́o; José Angel Rodrı́guez
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 660 KB
- Volume
- 125
- Category
- Article
- ISSN
- 0022-0396
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✦ Synopsis
Let H m be the space of planar homogeneous polynomial vector fields of degree m endowed with the coefficient topology. We characterize the set 0 m of the vector fields of H m that are structurally stable with respect to perturbations in H m and we determine the exact number of the topological equivalence classes in 0 m . The study of structurally stable homogeneous polynomial vector fields is very useful for understanding some interesting features of inhomogeneous vector fields. Thus, by using this characterization we can do first an extension of the Hartman Grobman Theorem which allows us to study the critical points of planar analytical vector fields whose k-jets are zero for all k<m under generic assumptions and second the study of the flows of the planar polynomial vector fields in a neighborhood of the infinity also under generic assumptions.