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Hofbauer, Franz

Examples for the nonuniqueness of the equilibrium state. (English) Zbl 0355.28010

Trans. Am. Math. Soc. 228, 223-241 (1977).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
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Cited in 44 Documents

MathOverflow Questions:

A unique equilibrium state which does not have Gibbs property

MSC:

28D05 Measure-preserving transformations
47A35 Ergodic theory of linear operators
54H20 Topological dynamics (MSC2010)
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References:

[1] Rufus Bowen, Equilibrium states and the ergodic theory of Anosov diffeomorphisms, Lecture Notes in Mathematics, Vol. 470, Springer-Verlag, Berlin-New York, 1975. · Zbl 0308.28010
[2] B. Felderhof and M. Fisher, four articles, Ann. Phys. 58 (1970), 176, 217, 268, 281.
[3] William Feller, An introduction to probability theory and its applications. Vol. I, John Wiley and Sons, Inc., New York; Chapman and Hall, Ltd., London, 1957. 2nd ed. · Zbl 0077.12201
[4] M. Fisher, Physica 3 (1967), 255-283.
[5] François Ledrappier, Principe variationnel et systèmes dynamiques symboliques, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 30 (1974), 185 – 202. · Zbl 0276.93004 · doi:10.1007/BF00533471
[6] David Ruelle, Statistical mechanics on a compact set with \?^{\?} action satisfying expansiveness and specification, Trans. Amer. Math. Soc. 187 (1973), 237 – 251. · Zbl 0278.28012
[7] Peter Walters, A variational principle for the pressure of continuous transformations, Amer. J. Math. 97 (1975), no. 4, 937 – 971. · Zbl 0318.28007 · doi:10.2307/2373682
[8] -, Ruelle’s operator theorem and g-measures, Trans. Amer. Math. Soc. (to appear).
[9] B. Weiss, Intrinsically ergodic systems, Bull. Amer. Math. Soc. 76 (1970), 1266 – 1269. · Zbl 0218.28011
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