The present note is aimed at proving an existence result of SRB measures for a class of topological Markov chains with infinitely many states, extending to saddle type sets previous results which generalizes several known versions of the Folklore Theorem to higher dimensional Markov transformations with infinitely many expanding branches. 
 
To the best of my knowledge these type of problems were considered for the first time by Newhouse and Jacobson. Here, as for Markov piecewise expanding endomorphisms, there is an essential difference between a finite and an infinite number of hyperbolic branches since derivatives grows to infinite with the number of branches so relations between the first and the second derivative become crucial.