Skip to main content
SpringerLink
Log in

Gibbs measures

  • Chapter
  • First Online:
Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms

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

  • 786 Accesses

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  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.

    Article  MathSciNet  Google Scholar 

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

    Article  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.

    Article  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.

    Article  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.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Authors
  1. Prof. Rufus Bowen
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1975 Springer-Verlag

About this chapter

Cite this chapter

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

Download citation

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

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07187-7

  • Online ISBN: 978-3-540-37534-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation