ASYMPTOTICS OF SIMPLE BRANCHING POPULATIONS

In this paper we study a simple deterministic tree structure: an initi al individual generates a finite number of offspring, each of which ha s given integer valued lifetime, iterating the same procedure when dyi ng. Three asymptotic distributions of this asynchronous deterministic branching procedure are considered: the generation distribution, the a bility of individuals to generate offspring and the age distribution. Thermodynamic formalism is then developed to reveal the multifractal n ature of the mass splitting associated to our process.