The prime orbit theorem and Mertens’ theorem are proved for a shift dynamical system of infinite type called the Dyck shift. Different and more direct methods are used in the proof without any complicated theoretical discussion.
Fahad Alsharari. Mohd Salmi Md. Noorani. Habibulla Akhadkulov. "Counting Closed Orbits for the Dyck Shift." Abstr. Appl. Anal. 2014 1 - 7, 2014. https://doi.org/10.1155/2014/304798