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

 

Boundaries of Markov partitions


Authors: Jonathan Ashley, Bruce Kitchens and Matthew Stafford
Journal: Trans. Amer. Math. Soc. 333 (1992), 177-201
MSC: Primary 58F15; Secondary 28D05, 54H20, 58F11
MathSciNet review: 1073772
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Abstract: The core of a Markov partition is the nonwandering set of the map restricted to the boundary of the partition. We show that the core of a Markov partition is always a finitely presented system. Then we show that every one sided sofic system occurs as the core of a Markov partition for an $ n$-fold covering map on the circle and every two sided sofic system occurs as the core of a Markov partition for a hyperbolic automorphism of the two dimensional torus.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1992-1073772-3
PII: S 0002-9947(1992)1073772-3
Keywords: Markov partitions, sofic systems
Article copyright: © Copyright 1992 American Mathematical Society