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

The abstract of the talk (see below) may be downloaded in one of the following formats:


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)\cap V\neq \emptyset
$, 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.


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