Abstract
We have already developed all the needed tools for doing the classification of topologically possible structurally unstable quadratic systems of codimension one∗. Along with the classification, we will discard many systems that are topologically possible; we can show their impossibility by means of their unfoldings or other criteria already described. Some phase portraits will pass these main filters and will appear as possible. However, we will discard some of them later on in Chap. 6 using more specific lemmas for each of them. We have preferred not to include these lemmas in this chapter or in Chap. 3 in order not to disturb the flow of this classification which is already quite long and tedious even this will force a renumbering of the cases.
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Artés, J.C., Llibre, J., Rezende, A.C. (2018). Proof of Theorem 1.1(a). In: Structurally Unstable Quadratic Vector Fields of Codimension One. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-92117-4_5
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DOI: https://doi.org/10.1007/978-3-319-92117-4_5
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