  Infinite Leslie matrices, introduced by Demetrius forty 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 to
models of self-reproducing machines and self-reproducing computer programs. The
dynamics of theses systems can also be described in terms of infinite Leslie
matrices.uation.
