ITES2001 Fourth Italian-Spanish conference on General Topology and its applications Bressanone, 27-30 June 2001

Transitivity of antitriangular maps

Antonio Linero Universidad de Murcia, Spain

We consider antitriangular maps, that is, two-dimensional continuous maps of the form F (x, y) = (g(y), f(x)), defined from the unit square into itself. This type of maps appears associated to an economical model so called Cournot duopoly. Recall that a continuous map f from a topological space X into itself is called topologically transitive if for any pair U, V of non-empty open sets of X, there exists a positive integer n such that f^{n}(U)∩V ≠ ∅, where f^{n} means the n–th iterate of f. We try to extend the properties of transitivity from one-dimensional maps to the antitriangular case. We obtain similar conclusions, with some difference as a consequence of dimension two.