Whenever a formal series $\textstyle f(X)=\sum_k f_k X^k \in R[[X]]$ has $f_0 = 0$ and $f_1$ being an invertible element of $R$, there exists a series $\textstyle g(X)=\sum_k g_k X^k$ that is the composition inverse of $f$, meaning that composing $f$ with $g$ gives the series representing the identity function (whose first coefficient is 1 and all other coefficients are zero). Ref.
What condition do the multivariate formal power series have composition inverse like one variable formal power series?
