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A Summary of Structurally Stable Quadratic Vector Fields

  • Joan C. Artés
  • Jaume Llibre
  • Alex C. Rezende
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Abstract

To make this work self-contained, we are going to summarize in this chapter all the needed results from the paper of Artés et al. (Mem. Am. Math. Soc. 134(639), 1998). For the results of the present paper, the realizable structurally stable quadratic vector fields and the non-realizable ones are very important. Therefore, we are going to describe all of them here. The technical lemmas have been included in Chap.  3 so we put here only the summary of the main result of Artés et al. (Mem. Am. Math. Soc. 134(639), 1998).

References

  1. 6.
    J.C. Artés, R. Kooij, J. Llibre, Structurally stable quadratic vector fields. Mem. Am. Math. Soc. 134(639), viii+108 (1998)Google Scholar
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    Y.Y. Quian, Theory of Limit Cycles. Translations of Mathematical Monographs, vol. 66, 2nd edn. (American Mathematical Society, Providence, 1984)Google Scholar
  3. 37.
    S. Songling, Topological classification of generic quadratic vector fields with no limit cycles. Report at the Third National Conference on Differential Equations (1965)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Joan C. Artés
    • 1
  • Jaume Llibre
    • 1
  • Alex C. Rezende
    • 1
  1. 1.Departament de MatemàtiquesUniversitat Autònoma de BarcelonaCerdanyolaSpain

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