Generating Function for Special Flows over the Countable $M$-Step Markov Chains

One way to classify some types of dynamical systems is comparing their entropies. A class of flows is called special flows which are conjugate to some types of flows on manifolds. Verifying the dynamical properties of flows such as computing their entropy is much easier when we deal with a special flow conjugate to the original one. In this paper we give a formula for computing the topological entropy of special flows when they are defined over a countable $M$-step Markov chain