Almost isomorphism for countable state Markov shifts
By Mike Boyle, Jérôme Buzzi, Ricardo Gómez. 2004
58 citations recorded by the source corpus.
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.
Subfields: Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/564b8a0ab470c425614de226d41260a7c7bc37f7
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In Computational Theory and Mathematics
In Mathematical Physics
Citations in the corpus
- Infinite alphabet edge shift spaces via ultragraphs and their C*-algebras (2017, background): “Further development of the theory appeared in [2, 3] where Boyle, Buzzi and Gómez study almost isomorphism for countable-state Markov shifts, [6, 20, 24, 27] where thermodynamical formalism for such shifts is developed, [28] where sliding block codes are characterized, and many other papers (see [25”