Skip to main content
Log in

Some systems with unique equilibrium states

  • Published:
Mathematical systems theory Aims and scope Submit manuscript

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. R. L. Adler andB. Weiss, Similarity of automorphisms of the torus,Memoirs of the A.M.S. no. 98, 1970.

  2. R. Bowen, Periodic points and measures for Axiom A diffeomorphisms,Trans. Amer. Math. Soc. 154 (1971), 377–397.

    Google Scholar 

  3. R. Bowen, Markov partitions for Axiom A diffeomorphisms,Amer. J. Math. 92 (1970), 725–747.

    Google Scholar 

  4. R. Bowen, Periodic orbits for hyperbolic flows,Amer. J. Math. 94 (1972), 1–30.

    Google Scholar 

  5. R. Bowen, The equidistribution of closed geodesics,Amer. J. Math. 94 (1972), 413–423.

    Google Scholar 

  6. R. Bowen, Maximizing entropy for hyperbolic flows,Math. Systems Theory 7 (1973), 300–303.

    Google Scholar 

  7. R. Bowen andP. Walters, Expansive one-parameter flows,J. Differential Equations 12 (1972), 180–193.

    Google Scholar 

  8. R. L. Dobrushin, Gibbsdian random fields for lattice systems with pairwise interactions,Functional Analysis and its Applications 2 (1968), 292–301.

    Google Scholar 

  9. R. L. Dobrushin, The problem of uniqueness of a Gibbsian random field and the problem of phase transitions,Functional Analysis and its Applications 2 (1968), 302–312.

    Google Scholar 

  10. R. L. Dobrushin, The description of a random field by means of conditional probabilities and conditions of its regularity,Theory of Probability and its Applications 13 (1968), 197–224.

    Google Scholar 

  11. K. Parathasarathy,Probability Measures on Metric Spaces, Academic Press, New York, 1967.

    Google Scholar 

  12. W. Parry, Intrinsic Markov chains,Trans. Amer. Math. Soc. 112 (1964), 55–66.

    Google Scholar 

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

    Google Scholar 

  14. D. Ruelle,Statistical Mechanics, Benjamin, New York, 1969.

    Google Scholar 

  15. D. Ruelle, Statistical mechanics on a compact set with Zvaction satisfying expansiveness and specification, preprint.

  16. Ja. G. Sinai, Mesures invariantes des Y-systems,Proc. Cong. Inter. Math. 1970, Vol. 2, 929–940.

    Google Scholar 

  17. S. Smale, Differentiable dynamical systems,Bull. Amer. Math. Soc. 73 (1967), 747–817.

    Google Scholar 

  18. B. Weiss, Intrinsically ergodic systems,Bull. Amer. Math. Soc. 76 (1970), 1226–1269.

    Google Scholar 

  19. B. Weiss, Subshifts of finite type and sofic systems, preprint.

  20. P. Billingsley,Ergodic Theory and Information, John Wiley and Sons, New York, 1965.

    Google Scholar 

  21. O. E. Lanford andD. Ruelle, Observables at infinity and states with short range correlations in statistical mechanics,Comm. Math. Phys. 13 (1969), 194–215.

    Google Scholar 

  22. O. E. Lanford andD. W. Robinson, Statistical mechanics of quantum spin systems III,Comm. Math. Phys. 9 (1968), 327–338.

    Google Scholar 

  23. O. E. Lanford, Entropy and equilibrium states in classical statistical mechanics,Proc. 1971 Battelle Rencontres in Mathematics and Physics, Lecture Notes, Physics Series, Springer-Verlag, Heidelberg.

  24. W. Krieger, On the uniqueness of the equilibrium state, preprint.

  25. H. Brascamp, Equilibrium states for a one dimensional lattice gas,Comm. Math. Phys. 21 (1971), 56–70.

    Google Scholar 

  26. R. Bowen Topological entropy and Axiom A,Proc. Symp. Pure Math., Vol. 14 (1970), 23–41.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Partially supported by NSF grant GP-14519.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bowen, R. Some systems with unique equilibrium states. Math. Systems Theory 8, 193–202 (1974). https://doi.org/10.1007/BF01762666

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01762666

Keywords

Navigation