Analogues of the Prime Number Theorem and Mertens' Theorem for Closed Orbits of the Motzkin Shift.

In this paper, the prime orbit theorem and Mertens' orbit theorem are proved for a shift dynamical system of infinite type called the Motzkin shift. Instead of using the zeta function approach to find the asymptotic formulas, different and more direct methods are used in the proof without any complicated theoretical discussion. [ABSTRACT FROM AUTHOR]