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Ergodicity and mixing via Young measures

Artstein, Z. and Grinfeld, M. (2002) Ergodicity and mixing via Young measures. Ergodic Theory and Dynamical Systems, 22 (4). pp. 1001-1015. ISSN 0143-3857

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Abstract

Connections are established between mixing or ergodic properties of maps on the one hand, and the convergence of the iterates of the map, or of the empirical measures of the iterates, to a constant measure-valued map, on the other. The uniqueness of an absolutely continuous ergodic measure can also be verified via the convergence. The technique helps to identify ergodic and mixing pairs and verify the uniqueness in specific examples.