Markov invariant dynamics

Abstract

We consider, , a certain class of Markov interval maps with domain contained in the interval I, whose associated transition matrix , necessarily primitive, plays a crucial role in the study of the underlying dynamics.

We study the problem of deciding when a restriction of a map to a subset is in the class , where is the minimal closed interval containing J. We establish natural conditions on so that is a Markov map. Then we tackle the central problem of deciding when the matrix is primitive in this framework. We are able to enumerate the sets J, satisfying the referred conditions, through a systematic process of elimination of the rows/columns of the state splitting of associated to the so called removable states, which ensures the primitivity of the matrices .