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Invariants of identity-tangent diffeomorphisms: explicit formulae and effective computation

In this short Survey we revisit the subject of local, identity-tangent diffeomorphisms of $\doC$ and their analytic invariants, under two viewpoints: that of explicit expansions, which necessarily involve multitangents and multizetas; and that of effective computation. Along the way, we stress the difference between the \textup{collectors} (pre-invariant but of one piece) and the \textup{connectors} (invariant but mutually unrelated). We also attempt to streamline the nomenclature and notations.