M. Golubitsky, E. Keeler and M. Rothschild
Convergence of the age structure: applications of the projective metric
Theor. Pop. Biol. 7 No. 1 (1975) 84-93.
This paper states necessary and sufficient conditions for the convergence
of the age structure (in a discrete time, one-sex model of population
growth); it also contains a new and simple proof of the weak ergodic
theorem of stable population theory. The main tool used to attain
these results is Hilbert's notion of the projective metric. This metric
provides a way of defining the distance between positive vectors in
R^n which has two important features: First, the distance between
any two positive vectors depends only on the rays on which the vectors
lie; and second, positive matrices act as contractions in this metric.