Integrability of vector fields versus inverse Jacobian multipliers and normalizers (Q325270)

In this interesting paper, the authors provide characterizations of integrability of finite families (systems) of vector fields in \(\mathbb{F}^n\), where \(\mathbb{F}=\mathbb{C}\) or \(\mathbb{R}\). The integrability of a family of \(k<n\) vector fields means the existence of \(n-k\) common first integrals which are functionally independent.NEWLINENEWLINEIn the last years appeared a series of deep results for vector fields (i.e., \(k=1\)) which provide characterizations of integrability via inverse Jacobian multipliers and normalizers. In order to extend them for arbitrary \(k\), the authors needed to introduce the notion of inverse Jacobian multiplier matrix for a finite family of vector fields, as a generalization of the notion of inverse Jacobian multiplier for a vector field.NEWLINENEWLINESome result add useful informations to the classical Frobenius integrability theorem.