Topological entropy of block maps

Source abstract

We show that h ( f ∞ ) = log ⁡ 2 h({f_\infty }) = \log 2 where f ∞ {f_\infty } is the map on the space of sequences of zeros and ones induced by the block map f ( x 0 , … , x k ) = x 0 + Π i = 1 k ( x i + b i ) f({x_0}, \ldots ,{x_k}) = {x_0} + \Pi _{i = 1}^k({x_i} + {b_i}) where k ⩾ 2 k \geqslant 2 and the k -block b 1 … b k {b_1} \ldots {b_k} is aperiodic.