\({\mathcal D}\)-envelope of a diffeomorphism of \((\mathbb C,0)\) (Q2484111)

Following the fundamental work of \textit{B. Malgrange} [Monogr. Enseign. Math. 38, 465-501 (2001; Zbl 1033.32020)], the author investigates \(D\)-envelopes of the local diffeomorphisms of a complex disc. In the first part of the paper, he gives a list of \(D\)-groupoids and proves that they are described by differential equations of order less then four. In the second part, he determines \(D\)-envelopes of diffeomorphisms and compares his classification with the one given by \textit{J. Ecalle} in his monograph [Publ. Math. Orsay 81-06, 248-531 (1981; Zbl 0499.30035)].