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

Author

Listed:
  • Azmeer Nordin

    (Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia
    These authors contributed equally to this work.)

  • Mohd Salmi Md Noorani

    (Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Azmeer Nordin & Mohd Salmi Md Noorani, 2020. "Orbit Growth of Periodic-Finite-Type Shifts via Artin–Mazur Zeta Function," Mathematics, MDPI, vol. 8(5), pages 1-19, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:685-:d:352790
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