Abstract
We discuss the connections between the existence of periodic points and the question of determining whether or not a (ℤ or ℤ2) Markov shift is empty and whether or not a given admissible block occurs in a point. We prove that if the Markov shift has a group structure then the periodic points are dense. This implies that in this class the extension problem is decidable.
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References
R. Berger, The Undecidability of the Domino Problem, Mem. AMS, No. 66, 1966.
B. Kitchens, Expansive Dynamics on Zero-dimensional Groups, to appear in Ergodic Theory and Dynamical Systems.
B. Kitchens and K. Schmidt, Automorphisms of Compact Groups, preprint.
R. Robinson, Undecidability and Nonperiodicity for Tilings of the Plane, Inventiones Math., Vol. 12, 1971.
H. Wang, Proving Theorems by Pattern Recognition-II, Bell System Tech. J., Vol. 40, 1961.
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© 1988 Springer-Verlag
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Kitchens, B., Schmidt, K. (1988). Periodic points, decidability and Markov subgroups. In: Alexander, J.C. (eds) Dynamical Systems. Lecture Notes in Mathematics, vol 1342. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0082845
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DOI: https://doi.org/10.1007/BFb0082845
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Print ISBN: 978-3-540-50174-9
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