Evolution: geometrical and dynamical aspects.

We develop a possible axiomatic approach to the evolution theory that has been previously discussed in Freguglia [2002]. The axioms synthesize the fundamental ideas of evolution theory and allow a geometrical and dynamical interpretation of the generation law. Using the axioms we derive a simple reaction-diffusion model which introduces the species as self-organized stationary distribution of a finite population and simulates the evolution of a phenotypic character under the effect of an external perturbing action. The dynamical properties of the model are briefly presented using numerical simulations.