On Sequence Entropy of Thue - Morse Shift

The paper summarizes properties of topological and sequence en- tropy of the Morse shift XM generated by the Thue-Morse sequence tM. The first part is an estimation of growth rate of possible subwords in tM. We show a polynomial upper bound on the number of finite subwords occuring in tM which is Cn2 log 3 for some constant C > 0. In the second part we prove that the sequence entropy of XM is achieved for the sequence τ (i) = 22i - 1.