"Siln\u00FD distribu\u010Dn\u00ED chaos a minim\u00E1ln\u00ED mno\u017Einy"@cs . . "Balibrea, Francisco" . "[5A3021222419]" . "6"^^ . "distributional chaos; minimal sets; triangular maps"@en . "Strong distributional chaos and minimal sets"@en . "RIV/47813059:19610/09:#0000225" . "Strong distributional chaos and minimal sets" . "RIV/47813059:19610/09:#0000225!RIV09-GA0-19610___" . . . "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 . "Strong distributional chaos and minimal sets"@en . "2"^^ . "344100" . "9" . "1"^^ . "Topology and its Applications" . "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." . "0166-8641" . . "19610" . . "NL - Nizozemsko" . . . . "156" . . "P(GA201/06/0318), Z(MSM4781305904)" . . "Siln\u00FD distribu\u010Dn\u00ED chaos a minim\u00E1ln\u00ED mno\u017Einy"@cs . "000265822300007" . . . "Ve t\u0159\u00EDd\u011B T troj\u00FAheln\u00EDkov\u00FDch zobrazen\u00ED \u010Dtverce zkoum\u00E1me nejsiln\u011Bj\u0161\u00ED verzi distribu\u010Dn\u00EDho chaosu, DC1, zaveden\u00E9ho Schweizerem a Sm\u00EDtalem [Trans. Amer. Math. Soc. 344 (1994) 737-854] pro spojit\u00E1 zobrazen\u00ED intervalu. Dokazujeme, \u017Ee existuje DC1 homeomorfizmus F z T takov\u00FD, \u017Ee ka\u017Ed\u00E1 omega-limitn\u00ED mno\u017Eina obsahuje jedinou minim\u00E1ln\u00ED mno\u017Einu. Homeomorfizmus je konstruov\u00E1n tak, \u017Ee je rostouc\u00ED na n\u011Bkter\u00FDch vl\u00E1knech a klesaj\u00EDc\u00ED na ostatn\u00EDch vl\u00E1knech. Proto m\u00E1 F nulovou topologickou entropii. Podobn\u00E9 chov\u00E1n\u00ED nen\u00ED mo\u017En\u00E9 pokud F je neklesaj\u00EDc\u00ED na v\u0161ech vl\u00E1knech, jak dok\u00E1zali Paganoni a Sm\u00EDtal [ Chaos Solitons Fractals 26 (2005) 581-589]. V\u00FDsledek je p\u0159\u00EDsp\u011Bvkem k \u0159e\u0161en\u00ED star\u00E9ho probl\u00E9mu Sharkovsk\u00E9ho, kter\u00FD se t\u00FDk\u00E1 klasifikace troj\u00FAheln\u00EDkov\u00FDch zobrazen\u00ED."@cs . . . . "Sm\u00EDtal, Jaroslav" . "Strong distributional chaos and minimal sets" . . .