Classification of permutations and cycles of maximum topological entropy (Q1431465)

A finite fully invariant set of a continuous map of a compact interval to itself induces a permutation in a natural way. If the invariant set is a periodic orbit the permutation is cyclic. Then one can calculate the topological entropy of any permutation \(\theta\) and it is well-known that this gives a lower bound for the topological entropy of any continuous selfmap of the interval which exhibits permutation of type \(\theta\). Here, the authors present cyclic and noncyclic permutations which have maximum topological entropy amongst all cyclic or noncyclic permutations of the same length.