Resumen de Topological Entropy and Adding Machine Maps

James Keesling, Louis Block

• We prove two theorems which extend known theorems concerning periodic orbits and topological entropy in one-dimensional dynamics. Our first result may be described as follows. Given a sequence of prime numbers, we form the corresponding adding machine map (also called the odometer map). We then determine the infimum of the topological entropies of all continuous maps of the interval which contain a copy of the given adding machine map. Our second result deals with the following question. Suppose we are given a closed subset of the interval and a continuous map of this closed subset to itself. How do we extend the given map to a map of the entire interval which has the smallest possible entropy?