Processing math: 100%
Regular and Chaotic Dynamics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Regul. Chaotic Dyn.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

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}
Linking options:
  • https://www.mathnet.ru/eng/rcd502
  • https://www.mathnet.ru/eng/rcd/v15/i2/p378
    • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Statistics & downloads:
    Abstract page:89
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025