Boundaries of Markov partitions

Ashley, Jonathan; Kitchens, Bruce; Stafford, Matthew

doi:10.1090/S0002-9947-1992-1073772-3

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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