The prime orbit theorem for quasihyperbolic toral automorphisms

DOI10.1007/BF01297343zbMath0737.28008MaRDI QIDQ1180718

Simon Waddington

Publication date: 27 June 1992

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/178542

zbMATH Keywords

prime number theoremalmost periodic functiontopological entropyclosed orbitsprime orbit theoremgeneric prime closed orbitquasihyperbolic toral automorphismsuniform distribution of periodic points

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Ergodic theory (37A99)

Related Items (15)

Estimates on the number of orbits of the Dyck shift ⋮ Asymptotic formulae for Lorenz and horseshoe knots ⋮ Closed orbits in quotient systems ⋮ A note on the growth of periodic points for commuting toral automorphisms ⋮ Counting closed orbits for the Dyck shift ⋮ Counting Closed Orbits in Discrete Dynamical Systems ⋮ Mertens’ theorem for toral automorphisms ⋮ Analogues of the prime number theorem and Mertens' theorem for closed orbits of the Motzkin shift ⋮ A dynamical zeta function for group actions ⋮ Orbit-counting in non-hyperbolic dynamical systems ⋮ Orbit growth for algebraic flip systems ⋮ A note on the dynamical zeta function of general toral endomorphisms ⋮ Counting finite orbits for the flip systems of shifts of finite type ⋮ Dirichlet series for finite combinatorial rank dynamics ⋮ Orbit growth of Dyck and Motzkin shifts via Artin–Mazur zeta function

Cites Work

• An analogue of the prime number theorem for closed orbits of Axiom A flows
• Dynamical properties of quasihyperbolic toral automorphisms
• Periodic Points and Measures for Axiom a Diffeomorphisms
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