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

DOI10.3934/dcds.2021046zbMath1477.37033OpenAlexW3137869442MaRDI QIDQ2042890

Azmeer Nordin, Mohd. Salmi Md. Noorani

Publication date: 22 July 2021

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2021046

zbMATH Keywords

shift of finite typeflip systemprime orbit counting function

Mathematics Subject Classification ID

Orbit growth in dynamical systems (37C35) Dynamics induced by group actions other than (mathbb{Z}) and (mathbb{R}), and (mathbb{C}) (37C85) Symbolic dynamics (37B10) Combinatorial dynamics (types of periodic orbits) (37E15)

Cites Work

• Estimates on the number of orbits of the Dyck shift
• Analogues of the prime number theorem and Mertens' theorem for closed orbits of the Motzkin shift
• 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
• A zeta function for flip systems.
• On periodic points
• Counting Closed Orbits in Discrete Dynamical Systems
• Dirichlet series for finite combinatorial rank dynamics
• Orbit-counting for nilpotent group shifts
• Functorial orbit counting
• Markov families for Anosov flows with an involutive action
• Orbit growth of Dyck and Motzkin shifts via Artin–Mazur zeta function
• On the number of fixed points of a sofic shift-flip system
• Orbit-counting in non-hyperbolic dynamical systems
• Orbit growth for algebraic flip systems
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