"1"^^ . "2" . . . . . "Li-Yorke sensitive minimal maps"@en . . . "RIV/47813059:19610/06:#0000050!RIV06-GA0-19610___" . "Nonlinearity" . "Li-Yorke sensitive minimal maps" . . "13"^^ . . "483472" . "\u010Ciklov\u00E1, Michaela" . . . . "RIV/47813059:19610/06:#0000050" . "19610" . . . . "0951-7715" . "517;529" . "[FF2E746146AA]" . "Li-Yorke sensitive; minimal set; triangular map; weak mixing system; spatio-temporally chaotic"@en . "Li-Yorkova senzitivita minim\u00E1ln\u00EDch funkc\u00ED"@cs . "1"^^ . . "Li-Yorke sensitive minimal maps" . "Nech\u0165 $Q$ je Cantorova mno\u017Eina, $S$ kru\u017Enice a $\\tau :Q\\rightarrowQ$ je zobrazen\u00ED adding machine. Na prostoru $X=Q\\times S$ uva\u017Eujme Euklidovu metriku. Uk\u00E1\u017Eeme, \u017Ee existuj\u00ED zobrazen\u00ED $F_i:X\\rightarrow X$, $F_i: (x,y)\\mapsto (\\tau (x), g_i(x,y))$, $i=1,2$ s n\u00E1sleduj\u00EDc\u00EDmi vlastnostmi: Oba syst\u00E9my $(X, F_1)$ i $(X, F_2)$ jsou minim\u00E1ln\u00ED bez slab\u011B mixuj\u00EDc\u00EDho faktoru (tzn. neexistuje semikonjugace do slab\u011B mixuj\u00EDc\u00EDho syst\u00E9mu). $(X, F_1)$ je spatio-temporally chaotick\u00FD, ale nen\u00ED Li-Yorkovsky senzitivn\u00ED. $(X, F_2)$ je Li-Yorkovsk\u00FD senzitivn\u00ED. Toto vyvrac\u00ED hypot\u00E9zy z \u010Dl\u00E1nku od E. Akina a S. Kolyady [Li-Yorke sensitivity, {\\it Nonlinearity} 16 (2003), 1421--1433]."@cs . "Let $Q$ be the Cantor middle third set, and $S$ the circle, and let $\\tau :Q\\rightarrow Q$ be an adding machine (i.e., odometer). Let $X=Q\\times S$ be equipped with (a metric equivalent to) the Euclidean metric. We show that there are continuous triangular maps $F_i: X\\rightarrow X$, $F_i: (x,y)\\mapsto (\\tau (x), g_i(x,y))$, $i=1,2$, with the following properties: Both $(X, F_1)$ and $(X, F_2)$ are minimal systems, without weak mixing factors (i.e., neither of them is semiconjugate to a weak mixing system). $(X, F_1)$ is spatio-temporally chaotic but not Li-Yorke sensitive. $(X,F_2)$ is Li-Yorke sensitive. This disproves conjectures of E. Akin and S. Kolyada [Li-Yorke sensitivity, {\\it Nonlinearity} 16 (2003), 1421--1433]."@en . . "P(GA201/03/1153), Z(MSM4781305904)" . . "GB - Spojen\u00E9 kr\u00E1lovstv\u00ED Velk\u00E9 Brit\u00E1nie a Severn\u00EDho Irska" . "Li-Yorke sensitive minimal maps"@en . . "19" . "Let $Q$ be the Cantor middle third set, and $S$ the circle, and let $\\tau :Q\\rightarrow Q$ be an adding machine (i.e., odometer). Let $X=Q\\times S$ be equipped with (a metric equivalent to) the Euclidean metric. We show that there are continuous triangular maps $F_i: X\\rightarrow X$, $F_i: (x,y)\\mapsto (\\tau (x), g_i(x,y))$, $i=1,2$, with the following properties: Both $(X, F_1)$ and $(X, F_2)$ are minimal systems, without weak mixing factors (i.e., neither of them is semiconjugate to a weak mixing system). $(X, F_1)$ is spatio-temporally chaotic but not Li-Yorke sensitive. $(X,F_2)$ is Li-Yorke sensitive. This disproves conjectures of E. Akin and S. Kolyada [Li-Yorke sensitivity, {\\it Nonlinearity} 16 (2003), 1421--1433]." . . "Li-Yorkova senzitivita minim\u00E1ln\u00EDch funkc\u00ED"@cs .