Weak Gibbs Measures for Intermittent Systems and Weakly Gibbsian States in Statistical Mechanics

Communications in Mathematical Physics

Volumn 241, Issue 2-3, 2003, Pages 453-466

  Yuri, Michiko ^a  

^a Sapporo University   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0242275983     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-003-0931-4     Document Type: Article

References (26)

1. Bowen, R.: Equilibrium states and the ergodic Theory of Anosov diffeomorphisms. Springer Lecture Notes in Mathematics 470, Berlin-Heidelberg-New York: Springer, 1975
2. v-action. Commun. Math. Phys. 48, 85-88 (1976)
3. Denker, M., Yuri, M.: A note on the construction of nonsingular Gibbs measures. Colloquium Mathematicum 84/85, 377-383 (2000)
4. Dobrushin, R.L.: A Gibbsian representation for non-Gibbsian fields. Workshop on Probability and Physics, Renkum, September 1995
5. Dobrushin, R.L., Shlosman, S.B.: Gibbsian description for non-Gibbsian fields. Russ. Math. Surveys 52, 285-297 (1997)
6. van.Enter, A.C.D., Fernandez, R., Sokal, A.D.: Regularity properties and pathologies of position-space renormalization transformations: Scope and limitations of Gibbsian theory. J. Stat. Phys. 72, 879-1167 (1993)
7. Keller, G.: Equilibrium states in Ergodic Theorey. Cambridge: Cambridge Univ. Press, 1998
8. Kozlov, O.K.: Gibbs description of a system of random variables. Probab. Inf. Transm. 10, 258-265 (1974)
9. Maes, C., Redig, F., Shlosman, S., Van. Moffaert, A.: Percolation, Path Large Deviations and weakly Gibbs States. Commun. Math. Phys. 208, 517-545 (2000)
10. Maes, C., Redig, F., Takens, F., Van. Moffaert, A., Verbitski, E.: Intermittency and weak Gibbs states. Nonlinearity 13, 1681-1698 (2000)
11. Maes, C., Redig, F., Van Moffaert, A.: Almost Gibbsian versus Weakly Gibbsian measures. Stoch. Proc. Appl. 79, 1-15 (1999)
12. Ruelle, D.: Thermodynamic formalism. Encyclopedia of Mathematics and its Applications 5, Reading MA: Addison-Wesley, 1978
13. Ruelle, D.: Thermodynamic formalism for maps satisfying positive expansiveness and specification. Nonlinearity 5, 1223-1236 (1992)
14. Schweiger, F.: Ergodic theory and fibred systems and metric number theory, Oxford: O.U.P., 1995
15. Sinai, Y.G.: Gibbs measures in ergodic theory. Russ. Math. Surv. 27, 21-70 (1972)
16. Walters, P.: Invariant measures and equilibrium states for some mappings which expand distances. Trans. Am. Math. Soc. 236, 121-153 (1978)
17. Yuri, M.: On a Bernoulli property for multi-dimensional mappings with finite range structure. Tokyo J. Math. 9, 457-485 (1986)
18. Yuri, M.: On the convergence to equilibrium states for certain nonhyperbolic systems. Ergodic Theory and Dyn. Syst. 17, 977-1000 (1997)
19. Yuri, M.: Zeta functions for certain nonhyperbolic systems and topological Markov approximations. Ergodic Theory and Dyn. Syst. 18, 1589-1612 (1998)
20. Yuri, M.: Thermodynamic formalism for certain nonhyperbolic maps. Ergodic Theory and Dyn. Syst. 19, 1365-1378 (1999)
21. Yuri, M.: Weak Gibbs measures for certain nonhyperbolic systems. Ergodic Theory and Dyn. Syst. 20, 1495-1518 (2000)
22. Yuri, M.: On the speed of convergence to equilibrium states for multi-dimensional maps with indifferent periodic points. Nonlinearity 15, 429-445 (2002)
23. Yuri, M.: Weak Gibbs measures and the local product structure. Ergodic Theory and Dyn. Syst. 22, 1933-1955 (2002)
24. Yuri, M.: Thermodynamic Formalism for countable to one Markov systems. Trans. Am. Math. Soc. 355, 2949-2971 (2003)
25. Yuri, M.: Multifractal analysis of weak Gibbs measures for intermittent systems. Commun. Math. Phys. 230, 365-388 (2002)
26. Yuri, M.: Phase transition, Non-Gibbsianness and Subexponential Instability. Preprint