which occurs in the theory of conformal mapping and univalent functions. In this case the ODEs are in the complex domain and differentiation is with respect to a complex variable. (The Schwarzian derivative S ( w ) has the remarkable property that it is invariant under Möbius transformations, i.e. S ( ( a w + b ) / ( c w + d ) ) = S ( w ) whenever a d − − b c is non-zero.) The function y = w ″ / w ′ satisfies the Riccati equation