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  • Ve třídě T trojúhelníkových zobrazení čtverce zkoumáme nejsilnější verzi distribučního chaosu, DC1, zavedeného Schweizerem a Smítalem [Trans. Amer. Math. Soc. 344 (1994) 737-854] pro spojitá zobrazení intervalu. Dokazujeme, že existuje DC1 homeomorfizmus F z T takový, že každá omega-limitní množina obsahuje jedinou minimální množinu. Homeomorfizmus je konstruován tak, že je rostoucí na některých vláknech a klesající na ostatních vláknech. Proto má F nulovou topologickou entropii. Podobné chování není možné pokud F je neklesající na všech vláknech, jak dokázali Paganoni a Smítal [ Chaos Solitons Fractals 26 (2005) 581-589]. Výsledek je příspěvkem k řešení starého problému Sharkovského, který se týká klasifikace trojúhelníkových zobrazení. (cs)
  • In the class T of triangular maps of the square we consider file strongest version of distributional chaos, DC1, introduced by Schweizer and Smital [Trans. Amer. Math. Soc. 344 (1994) 737-854] for continuous maps of the interval. We show that there is a DCI homeomorphism F z T such that any omega-limit set contains unique minimal set. This homeomorphism is constructed such that it is increasing on some fibres, and decreasing on the other ones. Consequently, F has zero topological entropy. Similar behavior is impossible when F is nondecreasing on the fibres, as shown by Paganoni and Smital [ Chaos Solitons Fractals 26 (2005) 581-589]. This result contributes to the solution of an old problem of Sharkovsky concerning classification of triangular maps.
  • In the class T of triangular maps of the square we consider file strongest version of distributional chaos, DC1, introduced by Schweizer and Smital [Trans. Amer. Math. Soc. 344 (1994) 737-854] for continuous maps of the interval. We show that there is a DCI homeomorphism F z T such that any omega-limit set contains unique minimal set. This homeomorphism is constructed such that it is increasing on some fibres, and decreasing on the other ones. Consequently, F has zero topological entropy. Similar behavior is impossible when F is nondecreasing on the fibres, as shown by Paganoni and Smital [ Chaos Solitons Fractals 26 (2005) 581-589]. This result contributes to the solution of an old problem of Sharkovsky concerning classification of triangular maps. (en)
Title
  • Strong distributional chaos and minimal sets
  • Silný distribuční chaos a minimální množiny (cs)
  • Strong distributional chaos and minimal sets (en)
skos:prefLabel
  • Strong distributional chaos and minimal sets
  • Silný distribuční chaos a minimální množiny (cs)
  • Strong distributional chaos and minimal sets (en)
skos:notation
  • RIV/47813059:19610/09:#0000225!RIV09-GA0-19610___
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GA201/06/0318), Z(MSM4781305904)
http://linked.open...iv/cisloPeriodika
  • 9
http://linked.open...vai/riv/dodaniDat
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  • 344100
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  • RIV/47813059:19610/09:#0000225
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  • distributional chaos; minimal sets; triangular maps (en)
http://linked.open.../riv/klicoveSlovo
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  • NL - Nizozemsko
http://linked.open...ontrolniKodProRIV
  • [5A3021222419]
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  • Topology and its Applications
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  • 156
http://linked.open...iv/tvurceVysledku
  • Balibrea, Francisco
  • Smítal, Jaroslav
http://linked.open...ain/vavai/riv/wos
  • 000265822300007
http://linked.open...n/vavai/riv/zamer
issn
  • 0166-8641
number of pages
http://localhost/t...ganizacniJednotka
  • 19610
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