A MEASURE OF SIMPLICITY FOR THE DYNAMICS OF AN ECONOMIC/BIOLOGICAL DISCRETE MODEL F. BALIBREA 1 , J. L. G. GUIRAO 2 AND F. L. PELAYO 3 1 Department of Mathematics, University of Murcia, 30100-Murcia. SPAIN 2 Department of Mathematics, 3 Department of Computer Science, University of Castilla-La Mancha, 16071 - Cuenca. SPAIN Abstract : - The aim of the current contribution is to present a topological characterization of dynamical simplicity for a discrete model which constitutes the mathematical environment of certain economic and biological processes. The tools used for obtaining it belong to the field of the topological dynamic of n-dimensional discrete systems. 1. Introduction and statement of the main result. Let X be a compact metric space and φ from X into itself be a continuous map (φ ∈C (X )). The pair (X,φ) is called the discrete dynamical sys- tem generated by φ on X . When X = I 2 (I = [0, 1]), there exists a class of maps D⊂C (I 2 ) such that the systems generated by its elements con- stitute the mathematical environment for describ- ing a very well-known economic production process called Cournot duopoly (see for instance [2], [6], [9] or [10]). The maps belonging to the class D are called Cournot maps and they are of the form φ(x,y)=(φ 1 (y),φ 2 (x)) where φ i ∈C (I ), i ∈{1, 2}. 2 Corresponding Author In order to have information about the economical situation previously described, these discrete mod- els has been studied from different points of view with the aim of describing their dynamical behav- ior (see for example [3], [5] or [8]). Specifically in [4], a topological characterization for their dy- namical complexity was given. This result is ex- actly the generalization for maps on D on one hand of the one-dimensional Misiurewicz´s theorem (see [7], (1) ⇔ (2)) and on other hand of certain re- sults proved by Sharkovski˘ ı in the sixties (see [12], (1) ⇔ (3) ⇔ (4)). By S n (·), Per(·), h(·), UR(·), Rec(·) and AP(·) we respectively denote a stratifi- cation set, the set of periods of periodic points, the topological entropy and the sets of uniformly recur- rent, recurrent and almost periodic points (see for 1