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Statements

Subject Item
n2:RIV%2F47813059%3A19610%2F06%3A%230000050%21RIV06-GA0-19610___
rdf:type
n6:Vysledek skos:Concept
dcterms:description
Nechť $Q$ je Cantorova množina, $S$ kružnice a $\tau :Q\rightarrowQ$ je zobrazení adding machine. Na prostoru $X=Q\times S$ uvažujme Euklidovu metriku. Ukážeme, že existují zobrazení $F_i:X\rightarrow X$, $F_i: (x,y)\mapsto (\tau (x), g_i(x,y))$, $i=1,2$ s následujícími vlastnostmi: Oba systémy $(X, F_1)$ i $(X, F_2)$ jsou minimální bez slabě mixujícího faktoru (tzn. neexistuje semikonjugace do slabě mixujícího systému). $(X, F_1)$ je spatio-temporally chaotický, ale není Li-Yorkovsky senzitivní. $(X, F_2)$ je Li-Yorkovský senzitivní. Toto vyvrací hypotézy z článku od E. Akina a S. Kolyady [Li-Yorke sensitivity, {\it Nonlinearity} 16 (2003), 1421--1433]. 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]. 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].
dcterms:title
Li-Yorkova senzitivita minimálních funkcí Li-Yorke sensitive minimal maps Li-Yorke sensitive minimal maps
skos:prefLabel
Li-Yorke sensitive minimal maps Li-Yorke sensitive minimal maps Li-Yorkova senzitivita minimálních funkcí
skos:notation
RIV/47813059:19610/06:#0000050!RIV06-GA0-19610___
n3:strany
517;529
n3:aktivita
n4:P n4:Z
n3:aktivity
P(GA201/03/1153), Z(MSM4781305904)
n3:cisloPeriodika
2
n3:dodaniDat
n10:2006
n3:domaciTvurceVysledku
n17:4988809
n3:druhVysledku
n5:J
n3:duvernostUdaju
n16:S
n3:entitaPredkladatele
n13:predkladatel
n3:idSjednocenehoVysledku
483472
n3:idVysledku
RIV/47813059:19610/06:#0000050
n3:jazykVysledku
n9:eng
n3:klicovaSlova
Li-Yorke sensitive; minimal set; triangular map; weak mixing system; spatio-temporally chaotic
n3:klicoveSlovo
n7:minimal%20set n7:spatio-temporally%20chaotic n7:triangular%20map n7:weak%20mixing%20system n7:Li-Yorke%20sensitive
n3:kodStatuVydavatele
GB - Spojené království Velké Británie a Severního Irska
n3:kontrolniKodProRIV
[FF2E746146AA]
n3:nazevZdroje
Nonlinearity
n3:obor
n12:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
1
n3:projekt
n14:GA201%2F03%2F1153
n3:rokUplatneniVysledku
n10:2006
n3:svazekPeriodika
19
n3:tvurceVysledku
Čiklová, Michaela
n3:zamer
n19:MSM4781305904
s:issn
0951-7715
s:numberOfPages
13
n15:organizacniJednotka
19610