Topological Entropy of Block Maps

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Apr 1980Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 78, page 590 (issn: 0002-9939,

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Authors: Coven, Ethan M.;

doi: 10.2307/2042437 , 10.1090/s0002-9939-1980-0556638-1

Topological Entropy of Block Maps

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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.

Keywords

Entropy in general topology, Topological dynamics, block map

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