Orbit-counting in non-hyperbolic dynamical systems
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Publication:5421681
DOI10.1515/CRELLE.2007.056zbMath1137.37006arXivmath/0511569OpenAlexW3104077842WikidataQ61835149 ScholiaQ61835149MaRDI QIDQ5421681
Shaun Stevens, Thomas B. Ward, Graham Everest, Richard B. Miles
Publication date: 24 October 2007
Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0511569
Topological dynamics (37B99) Distribution of primes (11N05) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30)
Related Items (13)
Estimates on the number of orbits of the Dyck shift ⋮ Counting closed orbits for the Dyck shift ⋮ Counting Closed Orbits in Discrete Dynamical Systems ⋮ Mertens’ theorem for toral automorphisms ⋮ Integer sequences and dynamics ⋮ Analogues of the prime number theorem and Mertens' theorem for closed orbits of the Motzkin shift ⋮ Dynamics on abelian varieties in positive characteristic ⋮ Uniform periodic point growth in entropy rank one ⋮ Counting finite orbits for the flip systems of shifts of finite type ⋮ Orbit-counting for nilpotent group shifts ⋮ Dirichlet series for finite combinatorial rank dynamics ⋮ Orbit growth of Dyck and Motzkin shifts via Artin–Mazur zeta function ⋮ Dold sequences, periodic points, and dynamics
Cites Work
- An analogue of the prime number theorem for closed orbits of Axiom A flows
- 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
- Agmon's Complex Tauberian Theorem and Closed Orbits for Hyperbolic and Geodesic Flows
- Almost all $S$-integer dynamical systems have many periodic points
- An Uncountable Family of Group Automorphisms, and a Typical Member
- Dynamical properties of quasihyperbolic toral automorphisms
- Group automorphisms with few and with many periodic points
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