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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Periodic points and automorphisms of the shift

Authors: Mike Boyle and Wolfgang Krieger
Journal: Trans. Amer. Math. Soc. 302 (1987), 125-149
MSC: Primary 54H20; Secondary 28D05, 54H15
MathSciNet review: 887501
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Abstract: The automorphism group of a topological Markov shift is studied by way of periodic points and unstable sets. A new invariant for automorphisms of dynamical systems, the gyration function, is used to characterize those automorphisms of finite subsystems of the full shift on $ n$ symbols which can be extended to a composition of involutions of the shift. It is found that for any automorphism $ U$ of a subshift of finite type $ S$, for all large integers $ M$ the map $ U{S^M}$ is a topological Markov shift whose unstable sets equal those of $ S$. This fact yields, by way of canonical measures and dimension groups, information about dynamical properties of $ U{S^k}$ such as the zeta function and entropy.

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PII: S 0002-9947(1987)0887501-5
Article copyright: © Copyright 1987 American Mathematical Society