Abstract
A topological system is universal for a class of ergodic measure-theoretic systems if its simplex of invariant measures contains, up to an isomorphism, all elements of this class and no elements from outside the class. We construct universal systems for classes given by the combination of three properties: measure-theoretic entropy belonging to a nondegenerate interval of the extended nonnegative real halfline, invertibility and aperiodicity. For classes consisting of aperiodic systems the universal system can be made minimal.
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