Orbit Growth of Periodic-Finite-Type Shifts via Artin–Mazur Zeta Function

Azmeer Nordin and Mohd Salmi Md Noorani
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Azmeer Nordin: Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia
Mohd Salmi Md Noorani: Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia

Mathematics, 2020, vol. 8, issue 5, 1-19

Abstract: The prime orbit and Mertens’ orbit counting functions describe the growth of closed orbits in a discrete dynamical system in a certain way. In this paper, we prove the asymptotic behavior of these functions for a periodic-finite-type shift. The proof relies on the meromorphic extension of its Artin–Mazur zeta function.

Keywords: periodic-finite-type shift; Artin–Mazur zeta function; prime orbit counting function; Mertens’ orbit counting functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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