Mathematical systems theory

, Volume 8, Issue 3, pp 193–202

Some systems with unique equilibrium states

  • Rufus Bowen


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    R. L. Adler andB. Weiss, Similarity of automorphisms of the torus,Memoirs of the A.M.S. no. 98, 1970.Google Scholar
  2. [2]
    R. Bowen, Periodic points and measures for Axiom A diffeomorphisms,Trans. Amer. Math. Soc. 154 (1971), 377–397.Google Scholar
  3. [3]
    R. Bowen, Markov partitions for Axiom A diffeomorphisms,Amer. J. Math. 92 (1970), 725–747.Google Scholar
  4. [4]
    R. Bowen, Periodic orbits for hyperbolic flows,Amer. J. Math. 94 (1972), 1–30.Google Scholar
  5. [5]
    R. Bowen, The equidistribution of closed geodesics,Amer. J. Math. 94 (1972), 413–423.Google Scholar
  6. [6]
    R. Bowen, Maximizing entropy for hyperbolic flows,Math. Systems Theory 7 (1973), 300–303.Google Scholar
  7. [7]
    R. Bowen andP. Walters, Expansive one-parameter flows,J. Differential Equations 12 (1972), 180–193.Google Scholar
  8. [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. [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. [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. [11]
    K. Parathasarathy,Probability Measures on Metric Spaces, Academic Press, New York, 1967.Google Scholar
  12. [12]
    W. Parry, Intrinsic Markov chains,Trans. Amer. Math. Soc. 112 (1964), 55–66.Google Scholar
  13. [13]
    D. Ruelle, Statistical mechanics of a one-dimensional lattice gas,Commun. Math. Phys. 9 (1968), 267–278.Google Scholar
  14. [14]
    D. Ruelle,Statistical Mechanics, Benjamin, New York, 1969.Google Scholar
  15. [15]
    D. Ruelle, Statistical mechanics on a compact set with Zvaction satisfying expansiveness and specification, preprint.Google Scholar
  16. [16]
    Ja. G. Sinai, Mesures invariantes des Y-systems,Proc. Cong. Inter. Math. 1970, Vol. 2, 929–940.Google Scholar
  17. [17]
    S. Smale, Differentiable dynamical systems,Bull. Amer. Math. Soc. 73 (1967), 747–817.Google Scholar
  18. [18]
    B. Weiss, Intrinsically ergodic systems,Bull. Amer. Math. Soc. 76 (1970), 1226–1269.Google Scholar
  19. [19]
    B. Weiss, Subshifts of finite type and sofic systems, preprint.Google Scholar
  20. [20]
    P. Billingsley,Ergodic Theory and Information, John Wiley and Sons, New York, 1965.Google Scholar
  21. [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. [22]
    O. E. Lanford andD. W. Robinson, Statistical mechanics of quantum spin systems III,Comm. Math. Phys. 9 (1968), 327–338.Google Scholar
  23. [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.Google Scholar
  24. [24]
    W. Krieger, On the uniqueness of the equilibrium state, preprint.Google Scholar
  25. [25]
    H. Brascamp, Equilibrium states for a one dimensional lattice gas,Comm. Math. Phys. 21 (1971), 56–70.Google Scholar
  26. [26]
    R. Bowen Topological entropy and Axiom A,Proc. Symp. Pure Math., Vol. 14 (1970), 23–41.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1975

Authors and Affiliations

  • Rufus Bowen
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

Personalised recommendations