Borel Isomorphism of SPR Markov Shifts

Mike Boyle (1) , Jerome Buzzi (2) , Ricardo Gomez (3)

1 Department of Mathematics
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay
3 Instituto de Matematicas [México]

We show that strongly positively recurrent Markov shifts (in particular shifts of finite type) are classified up to Borel conjugacy by their entropy, period and their numbers of periodic points.

Mots clés: entropy; Borel isomorphism; shift of finite type; countable state Markov shift; topological Markov chain; almost isomorphism

Domaines: Systèmes dynamiques [math.DS]

Mike Boyle, Jerome Buzzi, Ricardo Gomez. Borel Isomorphism of SPR Markov Shifts. 2014. ⟨hal-00997333⟩