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Mykola Matviichuk

Academician Glushkov pr. 2, Kyiv, 03127 Ukraine
Tereschenkivs’ka 3, Kyiv, 01601, Ukraine
Faculty of Mechanics and Mathematics, National Taras Shevchenko University of Kyiv
Institute of Mathematics, NASU


Matviichuk M.
On the set of periodic intervals of an interval map
2010, vol. 15, no. 2-3, pp.  378-381
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.
Keywords: dynamics of sets, periodic interval, interval map
Citation: Matviichuk M.,  On the set of periodic intervals of an interval map, Regular and Chaotic Dynamics, 2010, vol. 15, no. 2-3, pp. 378-381

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