QMW preprint DYN #91-9, Int. J. Bifurcation and Chaos, 2, 427--449, 1992

A CONICET (Consejo Nacional de Investigaciones Cientificas y Técnicas de Argentina) Fellow. Present address: Institut Nonlinéaire de Nice, Université de Nice---Sophia Antipolis, Parc Valrose, 06034 Nice Cédex, France.

We use the unorthodox notation 43#43 etc. to avoid any confusion with the iterates of a map.

A Mathematica package implementing Butcher's method for obtaining order conditions is now distributed as standard with version 2 of Mathematica.

n.b. The word `smoothness' is used here in its intuitive, nontechnical sense.

Julyan Cartwright
Wed Sep 27 17:21:22 MET 1995