Abstract
Following the classical procedure developed by Wiener and Ikehara for the proof of the prime number theorem we find an asymptotic formula for the number of closed orbits of a suspension of a shift of finite type when the suspended flow is topologically weak-mixing and when the suspending function is locally constant.
Article PDF
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
Avoid common mistakes on your manuscript.
References
L. M. Abramov,On the entropy of a flow, Dokl. Akad. Nauk SSSR128 (1959), 873–875 ≡ Am. Math. Soc., Transl. Ser. 2,49 (1966), 167–170.
R. Bhatia and K. K. Mukkerjea,On the rate of change of spectra of operators, Linear Algebra & Appl.27 (1979), 147–157.
R. Bowen,The equidistribution of closed geodesics, Am. J. Math.94 (1972), 413–423.
Su-shing Chen,Entropy of geodesic flow and exponent of convergence of some Dirichlet series, Math. Ann.255 (1981), 97–103.
Su-shing Chen and A. Manning,The convergence of zeta functions for certain geodesic flows depends on their pressure, Math. Z.176 (1981), 379–382.
G. A. Margulis,Applications of ergodic theory to the investigation of manifolds of negative curvature, Funkts. Anal. Prilozh.3 (4) (1969), 89–90.
W. Parry and S. Tuncel,Classification problems in ergodic theory, London Math. Soc. Lect. Note Ser. 67, Cambridge University Press, 1982.
D. Ruelle,Thermodynamic Formalism, Addison-Wesley, Reading, 1978.
N. Wiener,The Fourier Integral and Certain of its Applications, Cambridge University Press, 1967.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Parry, W. An analogue of the prime number theorem for closed orbits of shifts of finite type and their suspensions. Israel J. Math. 45, 41–52 (1983). https://doi.org/10.1007/BF02760669
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02760669