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Statements

Subject Item
n2:RIV%2F61988987%3A17610%2F10%3AA1100RIW%21RIV11-MSM-17610___
rdf:type
skos:Concept n16:Vysledek
dcterms:description
Let $\omega(\cdot)$ denote the union of all $\omega$-limit sets of a given map. As the main result of this paper we prove that, for given continuous interval maps $f_1,\ldots, f_m$, the set of $\omega$-limit points of the product map $f_1 \times \cdots \times f_m$ and the cartesian product of the sets $\omega(f_1),\ldots, \omega(f_m)$ coincide. This result substantially enriches the theory of multidimensional permutation product maps, i.e., maps of the form $F(x_1,\ldots, x_m) = (f_{\sigma(1)}(x_{\sigma(1)}), \ldots,f_{\sigma(m)}(x_{\sigma(m)}))$, where $\sigma$ is a permutation of the set of indices $\{1,\ldots,m\}$. Especially, for any such map $F$, we prove that the set $\omega(F)$ is closed and we also show that $\omega(F)$ cannot be a proper subset of the center of the map $F$. These results solve open questions mentioned, e.g., in [F. Balibrea, J. S. C\'{a}novas, A. Linero, {\em New results on topological dynamics of antitriangular maps\/}, Appl. Gen. Topol.]. Let $\omega(\cdot)$ denote the union of all $\omega$-limit sets of a given map. As the main result of this paper we prove that, for given continuous interval maps $f_1,\ldots, f_m$, the set of $\omega$-limit points of the product map $f_1 \times \cdots \times f_m$ and the cartesian product of the sets $\omega(f_1),\ldots, \omega(f_m)$ coincide. This result substantially enriches the theory of multidimensional permutation product maps, i.e., maps of the form $F(x_1,\ldots, x_m) = (f_{\sigma(1)}(x_{\sigma(1)}), \ldots,f_{\sigma(m)}(x_{\sigma(m)}))$, where $\sigma$ is a permutation of the set of indices $\{1,\ldots,m\}$. Especially, for any such map $F$, we prove that the set $\omega(F)$ is closed and we also show that $\omega(F)$ cannot be a proper subset of the center of the map $F$. These results solve open questions mentioned, e.g., in [F. Balibrea, J. S. C\'{a}novas, A. Linero, {\em New results on topological dynamics of antitriangular maps\/}, Appl. Gen. Topol.].
dcterms:title
On the $\omega$-limit sets of product maps On the $\omega$-limit sets of product maps
skos:prefLabel
On the $\omega$-limit sets of product maps On the $\omega$-limit sets of product maps
skos:notation
RIV/61988987:17610/10:A1100RIW!RIV11-MSM-17610___
n3:aktivita
n14:P n14:Z
n3:aktivity
P(1M0572), Z(MSM4781305904)
n3:cisloPeriodika
3-4
n3:dodaniDat
n19:2011
n3:domaciTvurceVysledku
n17:4033507
n3:druhVysledku
n9:J
n3:duvernostUdaju
n18:S
n3:entitaPredkladatele
n7:predkladatel
n3:idSjednocenehoVysledku
276894
n3:idVysledku
RIV/61988987:17610/10:A1100RIW
n3:jazykVysledku
n4:eng
n3:klicovaSlova
Discrete dynamical system; interval map; product map; permutation product map; antitriangular map; $\omega$-limit set; solenoidal set; basic set; center
n3:klicoveSlovo
n10:basic%20set n10:product%20map n10:%24%5Comega%24-limit%20set n10:interval%20map n10:center n10:Discrete%20dynamical%20system n10:antitriangular%20map n10:permutation%20product%20map n10:solenoidal%20set
n3:kodStatuVydavatele
US - Spojené státy americké
n3:kontrolniKodProRIV
[5911BFE0B0F9]
n3:nazevZdroje
Dynamic Systems and Applications
n3:obor
n12:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
3
n3:projekt
n6:1M0572
n3:rokUplatneniVysledku
n19:2010
n3:svazekPeriodika
19
n3:tvurceVysledku
Jiménez López, Victor Kupka, Jiří Linero, Antonio
n3:wos
000285265100019
n3:zamer
n8:MSM4781305904
s:issn
1056-2176
s:numberOfPages
12
n13:organizacniJednotka
17610