Topological entropy of block maps

Coven, Ethan M.

doi:10.1090/S0002-9939-1980-0556638-1

Topological entropy of block maps
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by Ethan M. Coven PDF

Proc. Amer. Math. Soc. 78 (1980), 590-594 Request permission

Abstract:

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

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A lower bound for the entropy of certain maps of the unit interval