Computing the topological entropy of continuous maps with at most three different kneading sequences with applications to Parrondo's paradox

We introduce an algorithm to compute the topological entropy of piecewise monotone maps with at most three different kneading sequences, with prescribed accuracy. As an application, we compute the topological entropy of 3-periodic sequences of logistic maps, disproving a commutativity formula for topological entropy with three maps, and analyzing the dynamics Parrondo's paradox in this setting.