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

DOI:
https://doi.org/10.1090/S0002-9947-1992-1073772-3

MathSciNet review:
1073772

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Abstract | References | Similar Articles | Additional Information

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 -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:
https://doi.org/10.1090/S0002-9947-1992-1073772-3

Keywords:
Markov partitions,
sofic systems

Article copyright:
© Copyright 1992
American Mathematical Society