Abstract
We give a new proof of the non uniqueness of the equilibrium state inF. Hofbauer's example. We extend it to obtain examples with any finite number of ergodic equilibrium states.
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Abramov, L. M.: Entropy of induced automorphisms. Dokl. Akad. Nauk. SSSR. 647–650 (1959).
Dyson, F. J.: Existence of a phase transition in a one dimensional ising ferromagnet. Commun. Math. Phys.12, 91–107 (1969).
Hofbauer, F.: Examples for the non-uniqueness of the equilibrium state. Trans. Amer. Math. Soc. (To appear.)
Israël, R. B.: Existence of phase transition for long-range interactions. Commun. Math. Phys.43, 59–68 (1975).
Kakutani, S.: Induced measure preserving transformations. Proc. Imp. Acad. Tokyo19, 635–641 (1943).
Krieger, W.: On the uniqueness of the equilibrium state. Math. Syst. Th.8, 97–104 (1974).
Neveu, J.: Une démonstration simplifiée et une extension de la formule d'Abramov sur l'entropie des transformations induites. Z. Wahrsch. verw. Geb.13, 135–140 (1969).
Shtil'man, M. S.: Number of invariant measures with maximal entropy for translation in the space of sequences. Mat. Zam.9, 291–302 (1971).
Walters, P.: A variationnal principle for the pressure of continuous transformations. Amer. J. Math.97, 937–971 (1975).
Walters, P.: Invariant measures and equilibrium states for some mappings which expand distances. Preprint.
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Ledrappier, F. Un Exemple de Transition de Phase. Monatshefte für Mathematik 83, 147–153 (1977). https://doi.org/10.1007/BF01534635
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DOI: https://doi.org/10.1007/BF01534635