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Abelian integrals in unfoldings of codimension 3 singular planar vector fields

Part I. The weakened 16-th Hilbert problem Part II. The saddle and elliptic cases Part III. The focus case

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Bifurcations of Planar Vector Fields

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1480))

Abstract

In this work it is shown that, for small βi, the system \(\dot x\)=y, \(\dot y\)=±x+αx 3+xy+β0+β1 y+β2 x 2 y has at most two limit cycles when α≠(−1/8, ∞)∖{0} (Part II) and also when α<−1/8 (Part III). Part I contains an introduction to the problem, applications of Abelian integrals and some general results.

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Authors
  1. Freddy Dumortier
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  2. Robert Roussarie
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  3. Jorge Sotomayor
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  4. Henryk Żaładek
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© 1991 Springer-Verlag

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Dumortier, F., Roussarie, R., Sotomayor, J., Żaładek, H. (1991). Abelian integrals in unfoldings of codimension 3 singular planar vector fields. In: Bifurcations of Planar Vector Fields. Lecture Notes in Mathematics, vol 1480. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0098361

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  • DOI: https://doi.org/10.1007/BFb0098361

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54521-7

  • Online ISBN: 978-3-540-38433-5

  • eBook Packages: Springer Book Archive

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