A. Linero

Periodic structure of alternating continuous interval maps

Given two continuous interval maps f and g, we study the periodic structure for the set of sequences generated by f and g by the rule . It is shown that this structure is intimately related to that of Sharkovskys Theorem, although some differences appear with the periods that are coprime with 2.

Topological dynamic classification of duopoly games

Abstract We classify Cournot maps on the unit square by using topological dynamics. More precisely, we prove that the following properties are equivalent: (1) zero topological entropy, (2) UR ( F )= R ( F ), (3) type less than or equal to 2 ∞ and (4) AP ( F )={( x , y )∈ I 2 :lim n →∞ F 2 n ( x , y )=( x , y )}. These results allow us to decide when the behavior of these two-dimensional dynamical systems is complicated.

On ω-limit sets of antitriangular maps☆

Abstract We give a topological characterization of ω-limit sets of continuous antitriangular maps, that is, maps F :[0,1] 2 →[0,1] 2 with the form F(x,y)=(f2(y),f1(x)), (x,y)∈I2. We also point out some differences between ω-limit set of antitriangular and one-dimensional maps.

SMOOTH TRIANGULAR MAPS OF TYPE 2∞ WITH POSITIVE TOPOLOGICAL ENTROPY

We explicitly construct for any k in ℕ a -differentiable triangular map in the square I2 with the following properties: (a) it has periodic orbits of period 2n for any n and no other periodic orbits, (b) the topological entropy is positive, and (c) the set of recurrent points contains properly the set of uniformly recurrent points.

Periodic structure of

Summary. We present a result concerning the periodic structure of certain maps on In = [0,1]n which are called

\sigma

\sigma

-permutations maps on In

-permutation maps. This structure resembles that given by the Šarkovskiis ordering for continuous interval maps.

On the global periodicity of some difference equations of third order

For we find all the p-cycles having the form , where are pairwise distinct and is continuous.

On the Periodic Structure of Delayed Difference Equations of the Form x n = f ( x n − k ) on I and S 1

The aim of this paper is to give an account of some results recently obtained in Combinatorial Dynamics and apply them to get for k S 2 the periodic structure of delayed difference equations of the form x n = f ( x n m k ) on I and S 1 .

Existence and uniqueness of p-cycles of second and third order

In this paper we obtain some new results about global periodicity of general difference equations of order two and three. To be more precise, we find: all the 4-cycles of the form , all the 6-cycles of type , and all the 3, 4 and 5-cycles of the form , where the mentioned continuous maps and the initial conditions are positive and most of the p-cycles obtained enjoy a potential form. We also prove that all the p-cycles of the form must verify g(x) = c/x for some c>0 constant, and p ≥ 5.