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2013
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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

## Publications:

 Matviichuk M. On the set of periodic intervals of an interval map 2010, vol. 15, no. 2-3, pp.  378-381 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. 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 DOI:10.1134/S156035471002022X