Mertens’ theorem for toral automorphisms

DOI10.1090/S0002-9939-2010-10632-9zbMath1232.37017arXiv0801.2082OpenAlexW3098846484WikidataQ60692423 ScholiaQ60692423MaRDI QIDQ3003592

Thomas B. Ward, Sawian Jaidee, Shaun Stevens

Publication date: 27 May 2011

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0801.2082

zbMATH Keywords

ergodic maptoral automorphismMerten's theoremquasihyperbolic map

Mathematics Subject Classification ID

Orbit growth in dynamical systems (37C35) Irrationality; linear independence over a field (11J72)

Related Items (6)

Estimates on the number of orbits of the Dyck shift ⋮ Closed orbits in quotient systems ⋮ Resolution of T. Ward's Question and the Israel–Finch Conjecture: Precise Analysis of an Integer Sequence Arising in Dynamics ⋮ Counting closed orbits for the Dyck shift ⋮ Counting Closed Orbits in Discrete Dynamical Systems ⋮ Analogues of the prime number theorem and Mertens' theorem for closed orbits of the Motzkin shift

Uses Software

• OEIS

Cites Work

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• The prime orbit theorem for quasihyperbolic toral automorphisms
• Heights of polynomials and entropy in algebraic dynamics
• An on-line version of ``The Encyclopedia of Integer Sequences
• Functorial orbit counting
• An analogue of Mertens' theorem for closed orbits of Axiom A flows
• Orbit-counting in non-hyperbolic dynamical systems

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