An obsolete term used to denote special birational transformations. The modern term is monoidal transformation.
There are, however, also several non-obsolete meanings of the term, such as the dilatation (dilatation coefficient) $k(f,a)$ of a quasi-conformal mapping and the theory of (unitary) dilatations in operator theory, cf. Contraction and Contraction semi-group; cf. also Spectral set.
Dilatation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Dilatation&oldid=31635