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First return map and invariant measures

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Abstract

We give sufficient conditions for the existence of absolutely continuous invariant measures, finite or σ-finite, for maps on the interval. We givea priori bound for the number of different ergodic measures. The results are obtained via the first return map.

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Authors and Affiliations

  1. Istituto Matematico “Ulisse Dini” Università di Firenze, Viale Morgagni 67/A, 50134, Firenze, Italy

    Giulio Pianigiani

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  1. Giulio Pianigiani
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Pianigiani, G. First return map and invariant measures. Israel J. Math. 35, 32–48 (1980). https://doi.org/10.1007/BF02760937

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  • DOI: https://doi.org/10.1007/BF02760937

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