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Gibbs measures

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Part of the Lecture Notes in Mathematics book series (LNM,volume 470)

Keywords

  • Statistical Mechanic
  • Gibbs Measure
  • Gibbs State
  • Gibbs Distribution
  • Nonempty Compact Convex Subset

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References

  1. R.L. Adler and B. Weiss, “Similarity of automorphisms of the torus”, Memoirs of the A.M.S. no. 98, 1970.

    Google Scholar 

  2. R. Bowen, “Some systems with unique equilibrium states”, Math. Systems Theory vol. 8, (1974).

    Google Scholar 

  3. R.L. Dobrushin, “The problem of uniqueness of a Gibbsian random field and the problem of phase transitions”, Func. Anal. and its Appl. 2 (1968), 302–312.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. N. Friedman and D. Ornstein, “On the isomorphism of weak Bernoulli transformations”, Advances in Math. 5 (1970), 365–394.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. G. Gallavotti, “Ising model and Bernoulli schemes in one dimension”, Commun. math. Phys. 32 (1973), 183–190.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. O. Lanford, “Entropy and equilibrium states in classical statistical mechanics”, statistical mechanics and mathematical problems (ed. A. Lenard), Springer-Verlag Lecture Notes in Physics, v.20.

    Google Scholar 

  7. O. Lanford and D. Ruelle, “Observables at infinity and states with short range correlations in statistical mechanics”, Commun. Math. Phys. 13 (1969), 194–215.

    CrossRef  MathSciNet  Google Scholar 

  8. A.N. Livshits, “Homology properties of Y-systems,” Math. Notes Acad. Sci. USSR 10 (1971), 758–763.

    CrossRef  MATH  Google Scholar 

  9. D. Ruelle, Statistical Mechanics, Benjamin.

    Google Scholar 

  10. -, “Statistical mechanics of a come-dimensional lattice gas”, Commun. Math. Phys. 9 (1968), 267–278.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. D. Ruelle, “A measure associated with Axiom A attractors,” Amer. J. Math.

    Google Scholar 

  12. Ya.G. Sinai, Gibbs measures in ergodic theory, Russian Math. Surveys no. 4 (166), 1972, 21–64.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. M. Ratner, “The central limit theorem for geodesic flows on n-dimensional manifolds of negative curvature, Israel J. Math. 16(1973), 181–197.

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1975 Springer-Verlag

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Bowen, R. (1975). Gibbs measures. In: Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms. Lecture Notes in Mathematics, vol 470. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0081281

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  • DOI: https://doi.org/10.1007/BFb0081281

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07187-7

  • Online ISBN: 978-3-540-37534-0

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