Population dynamics with infinite Leslie matrices: finite time properties

Infinite Leslie matrices, introduced by Demetrius 40 years ago, are mathematical models of age-structured populations defined by a countable infinite number of age classes. This article is concerned with determining solutions of the discrete dynamical system in finite time. We address this problem by appealing to the concept of kneading matrices and kneading determinants. Our analysis is applicable not only to populations models, but also to models of self-reproducing machines and self-reproducing computer programs. The dynamics of these systems can also be described in terms of infinite Leslie matrices.