About: Li-Yorke sensitive minimal maps

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Description	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]. (en) 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]. (cs)
Title	Li-Yorke sensitive minimal maps Li-Yorke sensitive minimal maps (en) Li-Yorkova senzitivita minimálních funkcí (cs)
skos:prefLabel	Li-Yorke sensitive minimal maps Li-Yorke sensitive minimal maps (en) Li-Yorkova senzitivita minimálních funkcí (cs)
skos:notation	RIV/47813059:19610/06:#0000050!RIV06-GA0-19610___
http://linked.open.../vavai/riv/strany	517;529
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA201/03/1153), Z(MSM4781305904)
http://linked.open...iv/cisloPeriodika	2
http://linked.open...vai/riv/dodaniDat	2006
http://linked.open...aciTvurceVysledku	Čiklová-Mlíchová, Michaela
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Slezská univerzita v Opavě / Matematický ústav v Opavě
http://linked.open...dnocenehoVysledku	483472
http://linked.open...ai/riv/idVysledku	RIV/47813059:19610/06:#0000050
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Li-Yorke sensitive; minimal set; triangular map; weak mixing system; spatio-temporally chaotic (en)
http://linked.open.../riv/klicoveSlovo	triangular map minimal set Li-Yorke sensitive spatio-temporally chaotic weak mixing system
http://linked.open...odStatuVydavatele	GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV	[FF2E746146AA]
http://linked.open...i/riv/nazevZdroje	Nonlinearity
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Dynamical systems II.
http://linked.open...UplatneniVysledku	2006
http://linked.open...v/svazekPeriodika	19
http://linked.open...iv/tvurceVysledku	Čiklová, Michaela
http://linked.open...n/vavai/riv/zamer	Topological and analytical methods in the theory of dynamical systems and mathematical physics
issn	0951-7715
number of pages	13 (xsd:int)
http://localhost/t...ganizacniJednotka	19610
is http://linked.open...avai/riv/vysledek of	Li-Yorke sensitive minimal maps Li-Yorke sensitive minimal maps

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