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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Boundaries of Markov partitions
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by Jonathan Ashley, Bruce Kitchens and Matthew Stafford PDF
Trans. Amer. Math. Soc. 333 (1992), 177-201 Request permission

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
  • © Copyright 1992 American Mathematical Society
  • 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