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eight-parameter families

Proceedings of the Edinburgh Mathematical Society (1)

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Centre manifold variety for eight-parameter families of polynomial vector fields of arbitrary degree
Part of
- Qualitative theory
- Stability theory
Clàudia Valls
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 53 / Issue 2 / June 2010

Published online by Cambridge University Press:

30 April 2010, pp. 511-530
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We characterize the centre variety of the eight-parameter families of real planar polynomial vector fields given, in complex notation, by , where A,B,C,D ∈ ℂ \{0}, (n1,j1) ≠ (n2,j2) ≠ (n3,j3) ≠ (n4,j4), nk + jk > 1 for k = 1,2,3,4, n1 + j1 = n2 + j2 = n3 + j3 = n4 + j4, |1 − n3 + j3| = |1 − n2 + j2| ≠ |1 − n1 + j1| and j4 = n4 − 1.