Given a vector field $Z \in \mathfrak{X}(M)$ on a $n$-dimensional manifold $M$ with a distinguished volume form $\Omega$, an inverse Jacobi multiplier (or inverse multiplier) is a smooth function $\Delta$ such that
$$ \sum_k Z_k \dfrac{\partial \Delta}{\partial x_k}=\Delta \mbox{div}(Z) $$or
$$ \frac{Z(\Delta)}{\Delta}=\mbox{div}(Z) $$See @berrone2003inverse page 14. But also, this is the definition given in @hu2015inverse for inverse integrating factor.
It is satisfied that if $\Delta$ is an inverse Jacobi multiplier then $1/\Delta$ is a Jacobi last multiplier.
It can be shown that the product of symmetrising factors is an inverse Jacobi multiplier. See the paper "symfactor", or the video 003 and xournal 199.
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Author of the notes: Antonio J. Pan-Collantes
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