Skip to main content
SpringerLink
Log in

Renewal theorems in symbolic dynamics, with applications to geodesic flows, noneuclidean tessellations and their fractal limits

  • Published:
Acta Mathematica

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Bowen, R.,Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms. Springer Lecture Notes in Mathematics, 470 (1975).

  2. —, Hausdorff dimension of quasicircles.Inst. Hautes Études Sci. Publ. Math., 50 (1979), 11–26.

    MATH  MathSciNet  Google Scholar 

  3. Feller, W.,An Introduction to Probability Theory and its Applications, vol. 2. Wiley, New York, 1966.

    MATH  Google Scholar 

  4. Ford, L. R.,Automorphic Functions. McGraw-Hill, New York, 1929.

    MATH  Google Scholar 

  5. Hejhal, D.,The Selberg Trace Formula for PSL(2,R). Springer Lecture Notes in Mathematics, 548 (1976).

  6. Huber, H., Über eine neue Klasse automorpher Functionen und eine Gitterpunktproblem in der hyperbolischen Ebene,Comment. Math. Helv., 30 (1956), 20–62.

    MathSciNet  Google Scholar 

  7. Hutchinson, J., Fractals and self similarity.Indiana Univ. Math. J., 30 (1981), 713–747.

    Article  MATH  MathSciNet  Google Scholar 

  8. Kato, T.,Perturbation Theory for Linear Operators. Springer-Verlag, New York, 1980.

    MATH  Google Scholar 

  9. Kolmogorov, A. N. &Tihomirov, V. M., Epsilon-entropy and epsilon-capacity of sets in functional spaces.Uspekhi Mat. Nauk, 14 (1959), 3–86.

    MathSciNet  MATH  Google Scholar 

  10. Krein, M. G., Integral equations on the half-line with a difference kernel.Uspekhi Mat. Nauk, 13 (1958), 3–120.

    MATH  Google Scholar 

  11. Lalley, S., Distribution of periodic orbits of symbolic and Axiom A flows.Adv. in Appl. Math., 8 (1987), 154–193.

    Article  MATH  MathSciNet  Google Scholar 

  12. —, Regenerative representation for one-dimensional Gibbs states.Ann. Probab., 14 (1986), 1262–1271.

    MATH  MathSciNet  Google Scholar 

  13. Lalley, S., Packing and covering functions of some self-similar fractals. Unpublished manuscript (1987).

  14. Lax, P. &Phillips, R., The asymptotic distribution of lattice points in euclidean and noneuclidean spaces.J. Funct. Anal., 46 (1982), 280–350.

    Article  MathSciNet  MATH  Google Scholar 

  15. Lehner, J.,Discontinuous Groups and Automorphic Functions, Amer. Math. Soc., Providence, 1964.

    MATH  Google Scholar 

  16. Mandelbrot, B.,The Fractal Geometry of Nature. Freeman, New York, 1983.

    Google Scholar 

  17. Margulis, G., Applications of ergodic theory to the investigation of manifolds of negative curvature.Funktsional. Anal. i Prilozhen, 3 (1969), 89–90.

    MATH  MathSciNet  Google Scholar 

  18. Nielsen, J., Untersuchungen zur Topologie der geschlossenen zweiseitigen Flächen.Acta Math., 50 (1927), 189–358.

    MATH  MathSciNet  Google Scholar 

  19. Parry, W., Bowen's equidistribution theorem and the Dirichlet density theorem.Ergodic Theory Dynamical Systems, 4 (1984), 171–134.

    MathSciNet  Google Scholar 

  20. Parry, W. &Pollicott, M., An analogue of the prime number theory for closed orbits of Axiom A flows.Ann. of Math., 118 (1983), 573–591.

    Article  MathSciNet  Google Scholar 

  21. Patterson, S. J., A lattice point problem in hyperbolic space.Mathematika 22 (1975), 81–88.

    Article  MATH  MathSciNet  Google Scholar 

  22. —, The limit set of a Fuchsian group.Acta Math., 136 (1976), 241–273.

    MATH  MathSciNet  Google Scholar 

  23. Pollicott, M., A complex Ruelle-Perron-Frobenius theorem and two counterexamples.Ergodic Theory Dynamical Systems, 4 (1984), 135–146.

    MATH  MathSciNet  Google Scholar 

  24. Rudolph, D., Ergodic behavior of Sullivan's geometric measure on a geometrically finite hyperbolic manifold.Ergodic Theory Dynamical Systems, 2 (1982), 491–512.

    MATH  MathSciNet  Google Scholar 

  25. Ruelle, D., Statistical mechanics of a one-dimensional lattice gas.Comm. Math. Phys., 9 (1968), 267–278.

    Article  MATH  MathSciNet  Google Scholar 

  26. —Thermodynamic Formalism. Addison-Wesley, Reading, 1978.

    MATH  Google Scholar 

  27. Series, C., The infinite word problem and limit sets in fuchsian groups.Ergodic Theory Dynamical Systems, 1 (1981), 337–360.

    MATH  MathSciNet  Google Scholar 

  28. —, Symbolic dynamics for geodesic flows.Acta Math., 146 (1981), 103–128.

    MATH  MathSciNet  Google Scholar 

  29. —, On coding geodesics with continued fractions.Enseign. Math., 29 (1981), 67–76.

    MATH  MathSciNet  Google Scholar 

  30. Sullivan, D., On the ergodic theory at infinity of an arbitrary discrete group of hyperbolic motions.Proc. Stony Brook Conf. Kleinian Groups and Reimann Surfaces, Princeton University Press (1978).

  31. —, The density at infinity of a discrete group of hyperbolic motions.Inst. Hautes Études Sci. Publ. Math., 50 (1979), 419–450.

    Google Scholar 

  32. —, Discrete conformal groups and measurable dynamics.Proc. Sympos. Pure Math., 39 (1983), 169–185.

    MATH  Google Scholar 

  33. —, Entropy, Hausdorff measures new and old, and limit sets of geometrically finite Kleinian groups.Acta Math., 153 (1984), 259–278.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Purdue University, West Lafayette, IN, USA

    Steven P. Lalley

Authors
  1. Steven P. Lalley
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lalley, S.P. Renewal theorems in symbolic dynamics, with applications to geodesic flows, noneuclidean tessellations and their fractal limits. Acta Math. 163, 1–55 (1989). https://doi.org/10.1007/BF02392732

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02392732

Keywords

Search

Navigation