Almost isomorphism for countable state Markov shifts

Mike Boyle, Jérôme Buzzi and Ricardo Gómez

Journal für die reine und angewandte Mathematik (Crelle's Journal)
592 (2006) 23-47.

Abstract. Countable state Markov shifts are a natural generalization of the well-known subshifts of finite type. They are the subject of current research both for their own sake and as models for smooth dynamical systems. In this paper, we investigate their almost isomorphism and entropy conjugacy and obtain a complete classification for the especially important class of strongly positive recurrent Markov shifts. This gives a complete classification up to entropy-conjugacy of the natural extensions of smooth entropy-expanding maps, e.g., C^∞ smooth interval maps with non-zero topological entropy.

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