Orbit growth of Dyck and Motzkin shifts via Artin–Mazur zeta function

DOI10.1080/14689367.2020.1770201zbMath1468.37023OpenAlexW3026193936MaRDI QIDQ4988836

Syahida Che Dzul-Kifli, Azmeer Nordin, Mohd. Salmi Md. Noorani

Publication date: 19 May 2021

Published in: Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/14689367.2020.1770201

zbMATH Keywords

Dyck shiftMotzkin shiftArtin-Mazur zeta functionprime orbit counting functionMertens' orbit counting functions

Mathematics Subject Classification ID

Orbit growth in dynamical systems (37C35) Zeta functions and (L)-functions (11S40) Relations between ergodic theory and number theory (37A44)

Related Items (1)

Counting finite orbits for the flip systems of shifts of finite type

Cites Work

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• Estimates on the number of orbits of the Dyck shift
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• An analogue of the prime number theorem for closed orbits of shifts of finite type and their suspensions
• The prime orbit theorem for quasihyperbolic toral automorphisms
• On periodic points
• Embedding of shifts of finite type into the Dyck shift
• Circular codes, loop counting, and zeta-functions
• Dirichlet series for finite combinatorial rank dynamics
• Functorial orbit counting
• An analogue of Mertens' theorem for closed orbits of Axiom A flows
• On the uniqueness of the equilibrium state
• Orbit-counting in non-hyperbolic dynamical systems

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