Interval maps from Cuntz–Krieger algebras

Markov interval maps f naturally produce transition aperiodic 0–1 matrices with extra features. We characterize the 0–1 matrices that can be realized as Markov transition matrices of interval maps, and parametrize the orbit representations (yielded in Correia Ramos et al. (2008) [2]) of the Cuntz–Krieger algebra O A obtained from interval maps with the same matrix A.