We show that strongly positively recurrent Markov shifts (including shifts of finite type) are classified up to Borel conjugacy by their entropy, period and their numbers of periodic points.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm137-1-9, author = {Mike Boyle and J\'er\^ome Buzzi and Ricardo G\'omez}, title = {Borel isomorphism of SPR Markov shifts}, journal = {Colloquium Mathematicae}, volume = {135}, year = {2014}, pages = {127-136}, zbl = {06356989}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm137-1-9} }
Mike Boyle; Jérôme Buzzi; Ricardo Gómez. Borel isomorphism of SPR Markov shifts. Colloquium Mathematicae, Tome 135 (2014) pp. 127-136. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm137-1-9/