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Generic properties of invariant measures for simple piecewise monotonic transformations

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Abstract

We endow the set of all invariant measures of topologically transitive subsetsL of certain piecewise monotonic transformations on [0, 1] with the weak topology. We show that the set of periodic orbit measures is dense, that the sets of ergodic, of nonatomic, and of measures with supportL are dense-sets, that the se of strongly mixing measures is of first category, and that the set of measures with zero entropy contains a denseGin/gd-set.

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  1. Institut für Mathematik, Universität Wien, Strudlhofgasse 4, A-1090, Wien, Austria

    Franz Hofbauer

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  1. Franz Hofbauer
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Hofbauer, F. Generic properties of invariant measures for simple piecewise monotonic transformations. Israel J. Math. 59, 64–80 (1987). https://doi.org/10.1007/BF02779667

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  • DOI: https://doi.org/10.1007/BF02779667

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