The commuting block maps problem
HTML articles powered by AMS MathViewer
- by Ethan M. Coven, G. A. Hedlund and Frank Rhodes PDF
- Trans. Amer. Math. Soc. 249 (1979), 113-138 Request permission
Abstract:
A block map is a map $f: {\{ {\text {0}}, {\text {1}}\} ^n} \to \{ 0, 1\}$ for some $n \geqslant 1$. A block map f induces an endomorphism ${f_\infty }$ of the full 2-shift $(X, \sigma )$. We define composition of block maps so that ${(f \circ g)_\infty } = {f_\infty } \circ {g_\infty }$. The commuting block maps problem (for f) is to determine $\mathcal {C}(f) = \{ g|f \circ g = g \circ f\}$. We solve the commuting block maps problem for a number of classes of block maps.References
-
J. D. Ferguson, Some properties of mappings on sequence spaces, Ph. D. Dissertation, Yale University, 1962.
- G. A. Hedlund, Endomorphisms and automorphisms of the shift dynamical system, Math. Systems Theory 3 (1969), 320–375. MR 259881, DOI 10.1007/BF01691062
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 249 (1979), 113-138
- MSC: Primary 54H20
- DOI: https://doi.org/10.1090/S0002-9947-1979-0526313-4
- MathSciNet review: 526313