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On the set of periodic intervals of an interval map

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Abstract

We investigate the closure of the set of periodic closed intervals for a continuous interval map with respect to Hausdorff metric. We prove that if a nondegenerate interval is limit of periodic ones then either a) it is periodic itself, or b) it is asymptotically degenerate, i.e. its diameter tends to 0 (when iterating under f). We present a continuous interval map for which case b) is possible.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, National Taras Shevchenko University of Kyiv, Academician Glushkov pr. 2, Kyiv, 03127, Ukraine

    M. Matviichuk

  2. Institute of Mathematics, NASU, Tereschenkivs’ka 3, Kyiv, 01601, Ukraine

    M. Matviichuk

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  1. M. Matviichuk
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Correspondence to M. Matviichuk.

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Matviichuk, M. On the set of periodic intervals of an interval map. Regul. Chaot. Dyn. 15, 378–381 (2010). https://doi.org/10.1134/S156035471002022X

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  • DOI: https://doi.org/10.1134/S156035471002022X

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