Resumen de Elementary proof of the continuity of the topological entropy at θ = 1001 −−−− in the Milnor-Thurston world
Andrés Jablonski, Rafael Labarca
In 1965, Adler, Konheim and McAndrew introduced the topological entropy of a given dynamical system, which consists of a real number that explains part of the complexity of the dynamics of the system. In this context, a good question could be if the topological entropy Htop(f) changes continuously with f. For continuous maps this problem was studied by Misisurewicz, Slenk and Urbański. Recently, and related with the lexicographic and the Milnor-Thurston worlds, this problem was studied by Labarca and others. In this paper we will prove, by elementary methods, the continuity of the topological entropy in a maximal periodic orbit (θ=1001−−−− ) in the Milnor-Thurston world. Moreover, by using dynamical methods, we obtain interesting relations and results concerning the largest eigenvalue of a sequence of square matrices whose lengths grow up to infinity.
