Normal forms and global phase portraits of quadratic and cubic integrable vector fields having two nonconcentric circles as invariant algebraic curves. Issue 3 (3rd July 2017) - Llibre, Jaume; Messias, Marcelo; Reinol, Alisson C.
ABSTRACT: In this paper, we give the normal form of all planar polynomial vector fields of degree d ≤ 3 having two nonconcentric circles C 1 and C 2 as invariant algebraic curves and the function, 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.