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Minimal ensembles without maximal entropy measures. (Ensembles minimaux sans mesure d’entropie maximale.) (French) Zbl 0358.28007

There has been a great deal of interest in recent years in the consideration of invariant measures for compact dynamical systems for which the measure theoretic entropy is equal to the topological entropy: measures with maximal entropy. In this paper the author constructs a compact minimal dynamical system with topological entropy equal to 1 and which has no measure with maximal entropy. The construction is a generalization of a construction described in section 27 of the lecture notes “Ergodic Theory in Compact Spaces” by M. Denker, C.Grillenberger, K.Sigmund [Lecture Notes Math. 527 (1976; Zbl 0328.28008)].
Reviewer: D. Newton

MSC:

28D05 Measure-preserving transformations
54H20 Topological dynamics (MSC2010)

Citations:

Zbl 0328.28008
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References:

[1] Denker, M., Ch. Grillenberger, andK. Sigmund: Ergodic theory on compact spaces. Lecture Notes in Math., Vol. 527. Berlin-Heidelberg-New York: Springer. 1976. · Zbl 0328.28008
[2] Grillenberger, Ch.: Constructions of strictly ergodic systems, I. Given entropy. z. Wahrsch.25, 323-334 (1973). · Zbl 0253.28004
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