Topological entropy and adding machine maps

We prove two theorems which extend known results concerning periodic orbits and topological entropy in one-dimensional dynamics. One of these results concerns the adding machine map (also called the odometer map) f(alpha) defined on the alpha-adic adding machine Delta(alpha). We let H(f(alpha)) denote the greatest lower bound of the topological entropies of F, taken over all continuous maps F of the interval which contain a copy of f(alpha). We prove that if alpha is a sequence of primes such that 2 appears in the sequence exactly k times, then H(f(alpha)) = log 2/2(k+1).