Skip to main content
Log in

Subshifts of quasi-finite type

  • Published:
Inventiones mathematicae Aims and scope

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

Access this article

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

Instant access to the full article PDF.

References

  1. Béal, M.-P., Mignosi, F., Restivo, A., Sciortino, M.: Forbidden words in symbolic dynamics, Adv. Appl. Math. 25, 163–193 (2000)

    Google Scholar 

  2. Berthé, V., Ferenczi, S., Mauduit, C., Siegel, A. (eds.): Substitutions in Dynamics, Arithmetics and Combinatorics. Lect. Notes Math., vol. 1794. Berlin: Springer 2002

  3. Bertrand, A.: Développement en base θ; répartition modulo un de la suite (xθn)n≥0; langages codés et θ-shift. Bull. Soc. Math. Fr. 114, 271–323 (1986)

    Google Scholar 

  4. Bertrand, A.: Specification, synchronisation, average length. In: Coding Th. and applications (Cachan 1986), pp. 86–95. Lect. Notes Comput. Sci., vol. 311. Berlin: Springer 1988

  5. Blanchard, F., Hansel, G.: Systèmes codés. Theor. Comput. Sci. 44, 17–49 (1986)

    Article  MathSciNet  Google Scholar 

  6. Bowen, R.: Some systems with unique equilibrium states. Math. Systems Theory 8, 193–202 (1974/75)

  7. Boyle, M., Buzzi, J., Gomez, R.: Almost isomorphism for countable state Markov shifts. Preprint CMAT 2004

  8. Buzzi, J.: Intrinsic ergodicity of smooth interval maps. Isr. J. Math. 100, 125–161 (1997)

    Article  MathSciNet  Google Scholar 

  9. Buzzi, J.: Specification on the interval. Trans. Am. Math. Soc. 349, 2737–2754 (1997)

    Article  MathSciNet  Google Scholar 

  10. Buzzi, J.: Intrinsic ergodicity of affine maps in [0,1]d. Monatsh. Math. 124, 97–118 (1997)

    Article  MathSciNet  Google Scholar 

  11. Buzzi, J.: Markov extensions for multi-dimensional dynamical systems. Isr. J. Math. 112, 357–380 (1999)

    Article  MathSciNet  Google Scholar 

  12. Buzzi, J.: On entropy-expanding maps. Preprint CMAT 2000

  13. Denker, M., Grillenberger, C., Sigmund, K.: Ergodic theory on compact spaces, Lect. Notes Math., vol. 527. Berlin, New York: Springer 1976

  14. Flatto, L., Lagarias, J.C.: The lap-counting function for linear mod one transformations. I. Explicit formulas and renormalizability. Ergodic Theory Dyn. Syst. 16, 451–491 (1996)

    MathSciNet  Google Scholar 

  15. Gurevich, B.M.: Shift entropy and Markov measures in the path space of a denumerable graph. Soviet Math. Dokl. 3, 744–747 (1970)

    Google Scholar 

  16. Gurevich, B.M.: Uniqueness of the measure with maximal entropy for symbolic dynamical systems that are close to Markov ones. Soviet Math. Dokl. 13, 569–571 (1972)

    Google Scholar 

  17. Gurevich, B.M.: Stably recurrent nonnegative matrices. Russ. Math. Surv. 51, 551–552 (1996)

    Article  Google Scholar 

  18. Gurevich, B.M., Savchenko, S.: Thermodynamic formalism for symbolic Markov chains with a countable number of states. Russ. Math. Surv. 53, 245–344 (1998)

    Article  Google Scholar 

  19. Hadamard, J.: Les surfaces à courbures opposées et leurs lignes géodésiques. J. Math. Pures Appl. 4, 27–73 (1898)

    Google Scholar 

  20. Hofbauer, F.: β-shifts have unique maximal measure. Monatsh. Math. 85, 189–198 (1978)

    Article  MathSciNet  Google Scholar 

  21. Hofbauer, F.: On intrinsic ergodicity of piecewise monotonic transformations with positive entropy. Isr. J. Math. 34, 213–237 (1979)

    Article  MathSciNet  Google Scholar 

  22. Hofbauer, F., Keller, G.: Zeta-functions and transfer operators for piecewise linear transformations. J. Reine Angew. Math. 352, 100–113 (1984)

    MathSciNet  Google Scholar 

  23. Ito, Sh., Murata, H., Totoki, H.: Remarks on the isomorphism theorem for weak Bernoulli transformations in the general case. Publ. Res. Inst. Math. Sci. 7, 541–580 (1971/1972)

  24. Kahane, J.-P.: Hadamard et la stabilité du système solaire. Travaux mathématiques, Fasc. XI (Luxembourg, 1998), pp. 33–48. Luxembourg: Centre Univ. Luxembourg 1999

  25. Keller, G.: Lifting measures to Markov extensions. Monatsh. Math. 108, 183–200 (1989)

    Article  MathSciNet  Google Scholar 

  26. Kitchens, B.: Symbolic dynamics. One-sided, two-sided and countable state Markov shifts. Berlin: Springer 1998

  27. Krieger, W.: On the uniqueness of the equilibrium state. Math. Systems Theory 8, 97–104 (1974/75)

  28. Krieger, W.: On subshifts and topological Markov chains. Numbers, information and complexity, ed. by I. Althöfer et al., pp. 453–472. Kluwer Academic Publishers 2000

  29. Kwapisz, J.: Cocyclic subshifts. Math. Z. 234, 255–290 (2000)

    Article  MathSciNet  Google Scholar 

  30. Kwapisz, J.: Transfer operator, topological entropy and maximal measure for cocyclic subshifts. Preprint 2001, http://www.math.montana.edu/∼jarek. To appear in Ergodic Theory Dyn. Syst.

  31. Lind, D., Marcus, B.: An introduction to symbolic dynamics and coding. Cambridge: Cambridge University Press 1995

  32. de Melo, W., van Strien, S.: One-dimensional dynamics. Ergebnisse der Mathematik und ihrer Grenzgebiete (3), 25. Berlin: Springer 1993

  33. Parry, W., Pollicot, M.: Zeta functions and the periodic orbit structure of hyperbolic dynamics. Astérisque 187188 (1990)

  34. Petersen, K.: Chains, entropy, coding. Ergodic Theory Dyn. Syst. 6, 415–448 (1986)

    Article  Google Scholar 

  35. Rudolph, D.: Fundamentals of measurable dynamics. Ergodic theory on Lebesgue spaces. New York: Oxford University Press 1990

  36. Salama, I.: On the recurrence of countable topological Markov chains. In: Symbolic dynamics and its applications (New Haven, CT, 1991), pp. 349–360. Contemp. Math. 135. Providence, RI: Amer. Math. Soc. 1992

  37. Schmeling, J.: Symbolic dynamics for β-shifts and self-normal numbers. Ergodic Theory Dyn. Syst. 17, 675–694 (1997)

    Article  MathSciNet  Google Scholar 

  38. Shub, M.: Global stability of dynamical systems. New York: Springer 1987

  39. Szymczak, A.: The Conley index and symbolic dynamics. Topology 35, 287–299 (1996)

    Article  MathSciNet  Google Scholar 

  40. Takahashi, Y.: Isomorphisms of β-automorphisms to Markov automorphisms. Osaka J. Math. 10, 175–184 (1973)

    MathSciNet  Google Scholar 

  41. Vere-Jones, D.: Ergodic properties of nonnegative matrices I. Pac. J. Math. 22, 361–386 (1967)

    Article  MathSciNet  Google Scholar 

  42. Walters, P.: An introduction to ergodic theory. Graduate Texts in Mathematics, vol. 79. New York: Springer 1982

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jérôme Buzzi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Buzzi, J. Subshifts of quasi-finite type. Invent. math. 159, 369–406 (2005). https://doi.org/10.1007/s00222-004-0392-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00222-004-0392-1

Keywords

Navigation