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Regular and Chaotic Dynamics, 2010, Volume 15, Issue 2-3, Pages 378–381
DOI: https://doi.org/10.1134/S156035471002022X (Mi rcd502) 		 
On the 75th birthday of Professor L.P. Shilnikov

On the set of periodic intervals of an interval map

M. Matviichukab

a Faculty of Mechanics and Mathematics, National Taras Shevchenko University of Kyiv, Academician Glushkov pr. 2, Kyiv, 03127 Ukraine
b Institute of Mathematics, NASU, Tereschenkivs’ka 3, Kyiv, 01601 Ukraine
DOI: https://doi.org/10.1134/S156035471002022X
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.
Received: 22.12.2009
Accepted: 25.01.2010
Bibliographic databases:
Document Type: Personalia
MSC: 37E99
Language: English
Citation: M. Matviichuk, “On the set of periodic intervals of an interval map”, Regul. Chaotic Dyn., 15:2-3 (2010), 378–381
Citation in format AMSBIB
\Bibitem{Mat10}
\by M. Matviichuk
\paper On the set of periodic intervals of an interval map
\jour Regul. Chaotic Dyn.
\yr 2010
\vol 15
\issue 2-3
\pages 378--381
\mathnet{http://mi.mathnet.ru/rcd502}
\crossref{https://doi.org/10.1134/S156035471002022X}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2644344}
\zmath{https://zbmath.org/?q=an:1203.37077}
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