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Structural Stability of Planar Polynomial Foliations |
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| Authors: | |
| Institution: | (1) Department de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via, 585, 08007 Barcelona, Spain;(2) Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain;(3) Mathematics Department, University of North Carolina at Charlotte, Charlotte, NC 28223, USA |
| Abstract: | We discuss natural notions of structural stability of planar polynomial foliations of fixed degree with respect to perturbation within the same restricted set, within the set of all polynomial vector fields of the same degree, and within the set of smooth vector fields. Characterization theorems for structural stability in the latter two settings are obtained as immediate corollaries of known results. We provide sufficient conditions and separate necessary conditions for structural stability of planar polynomial foliations with respect to perturbation within the set of planar polynomial foliations of the same degree. |
| Keywords: | Foliation polynomial vector field structural stability |
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