© 2016 Informa UK Limited, trading as Taylor & Francis Group. In this paper, we give the normal form of all planar polynomial vector fields of degree d ≤ 3 having two nonconcentric circles C1 and C2 as invariant algebraic curves and the function H=Cβ1 Cα2, with α and β real values, as first integral. Moreover, we classify all global phase portraits on the Poincaré disc of a subclass of these vector fields.
|Publication status||Published - 3 Jul 2017|
- Poincaré compactification
- Quadratic and cubic vector fields
- global analysis
- invariant algebraic curves
- limit cycles
- normal forms