Abstract
The vector-valued function m( ) of a p-vector has components m1( );m2( );:::;mp( ). For eachi, exp(mi( )) is the (multivariate) Laplace transform of a discrete measure concentrated on (0;1) p with only a nite number of atoms. The main objective is to give conditions for the functional iteratesm(n) ofm to grow like n for a suitable > 1. The initial stimulus was provided by results of Miller and O'Sullivan (1992) on enumeration issues in 'context free languages', results which can be improved using the theory devel- oped here. The theory also allow certain results in Jones (2004) on multitype branching to be proved under signicantly weaker conditions.
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