<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">V. JIMÉNEZ LÓPEZ</style></author><author><style face="normal" font="default" size="100%">J. KUPKA</style></author><author><style face="normal" font="default" size="100%">A. LINERO</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON THE ω-LIMIT SETS OF PRODUCT MAPS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">37B99</style></keyword><keyword><style  face="normal" font="default" size="100%">37E05</style></keyword><keyword><style  face="normal" font="default" size="100%">37E99</style></keyword><keyword><style  face="normal" font="default" size="100%">54H20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/47-DSA-182.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Let ω(·)&amp;nbsp; denote the union of all ω-limit sets of a given map. As the main result of this paper we prove that, for given continuous interval maps f&lt;sub&gt;1&lt;/sub&gt;, . . . , f&lt;sub&gt;m&lt;/sub&gt;, the union of all ω-limit sets of the product map f&lt;sub&gt;1&lt;/sub&gt; × · · · × fm and the cartesian product of the sets ω(f&lt;sub&gt;1&lt;/sub&gt;), . . . , ω(f&lt;sub&gt;m&lt;/sub&gt;) coincide. This result enriches the theory of multidimensional permutation product maps, i.e., maps of the form F( x&lt;sub&gt;1&lt;/sub&gt;, . . . , x&lt;sub&gt;m&amp;nbsp;&lt;/sub&gt;) = ( f&lt;sub&gt;σ(1) &lt;/sub&gt;(x&lt;sub&gt;σ(1)&lt;/sub&gt;), . . . , f&lt;sub&gt;σ(m)&lt;/sub&gt;(x&lt;sub&gt;σ(m)&lt;/sub&gt;) ), where σ is a permutation of the set of indices {1, . . . , m}. For any such map F, we prove that the set ω(F) is closed and we also show that ω(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. Cánovas, A. Linero, New results on topological dynamics of antitriangular maps, Appl. Gen. Topol.].&lt;/p&gt;
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