Periodic seeded arrays and automorphisms of the shift

Author:
Ezra Brown

Journal:
Trans. Amer. Math. Soc. **339** (1993), 141-161

MSC:
Primary 58F03; Secondary 28D20, 54H20

DOI:
https://doi.org/10.1090/S0002-9947-1993-1145960-X

MathSciNet review:
1145960

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Abstract: The automorphism group of the full -shift is conjectured to be generated by the shift and involutions. We approach this problem by studying a certain family of automorphisms whose order was unknown, but which we show to be finite and for which we find factorizations as products of involutions. The result of this investigation is the explicit construction of a subgroup of ; is generated by certain involutions , and turns out to have a number of curious properties. For example, and commute unless and are consecutive integers, the order of is independent of , and contains elements of all orders. The investigation is aided by the development of results about certain new types of arrays of 0's and 's called periodic seeded arrays, as well as the use of Boyle and Krieger's work on return numbers and periodic points.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1993-1145960-X

Keywords:
Block maps,
shift dynamical system,
automorphism group,
symbolic dynamics,
arrays,
periodic points

Article copyright:
© Copyright 1993
American Mathematical Society