On the $omega$-limit sets of product maps

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F10%3AA1100RIW" target="_blank" >RIV/61988987:17610/10:A1100RIW - isvavai.cz</a>
Alternative codes found
RIV/47813059:19610/10:#0000281
Result on the web
—
DOI - Digital Object Identifier
—

Result language
angličtina
Original language name
On the $omega$-limit sets of product maps
Original language 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.].
Czech name
—
Czech description
—

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/1M0572" target="_blank" >1M0572: Data, algorithms, decision making</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2010
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)