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Centre manifold variety for eight-parameter families of polynomial vector fields of arbitrary degree

Part of: Stability theory Qualitative theory

Published online by Cambridge University Press:  30 April 2010

Clàudia Valls
Clàudia Valls
Affiliation:
Departamento de Matemática, Instituto Superior Técnico, Avenida Rovisco Pais, 1049001 Lisboa, Portugal ([email protected])
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Abstract

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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.

Keywords

centresarbitrary degreepolynomial vector fieldseight-parameter families

MSC classification

Secondary: 34C25: Periodic solutions 34D30: Structural stability and analogous concepts
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 53 , Issue 2 , June 2010 , pp. 511 - 530
Copyright
Copyright © Edinburgh Mathematical Society 2010