  Let $F(z)=z-H(z)$ with $o(H(z))\geq 2$ be a formal map from $\bC^n$ to
$\bC^n$ and $G(z)$ the formal inverse of $F(z)$. In this paper, we fist study
the deformation $F_t(z)=z-tH(z)$ and its formal inverse map $G_t(z)$. We then
derive two recurrent formulas for the formal inverse $G(z)$. The first formula
in certain situations provides a more efficient method for the calculation of
$G(z)$ than other well known inversion formulas. The second one is differential
free but only works when $H(z)$ is homogeneous of degree $d\geq 2$. Finally, we
reveal a close relationship of the inversion problem with a Cauchy problem of a
PDE. When the Jacobian matrix $JF(z)$ is symmetric, the PDE coincides with the
$n$-dimensional inviscid Burgers' equation in Diffusion theory.
