<?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%">SHAFIQUL ISLAM</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A FAMILY OF RANDOM MAPS WHICH POSSES INFINITE ABSOLUTELY CONTINUOUS INVARIANT MEASURES</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%">37A05</style></keyword><keyword><style  face="normal" font="default" size="100%">37H10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">09/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/4/3.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;We consider a family of random maps where each of the component&amp;nbsp;maps is from a family of piecewise, linear and Markov maps on a class of infinite&amp;nbsp;partitions of the state space. We investigate the existence of infinite absolutely continuous&amp;nbsp;invariant measures of the random maps. In a more general setting, our study&amp;nbsp;establishes a positive answer to the question in discrete time dynamical system: can&amp;nbsp;two chaotic systems give rise to order, namely can they be combined into another&amp;nbsp;dynamical system which does not behave chaotically? This question is analogous to&amp;nbsp;Parrondo’s paradox [5] which states that two losing gambling games when combined&amp;nbsp;one after the other (either deterministically or randomly) can result in a winning&amp;nbsp;game: that is, a losing game followed by a losing game = a winning game.&lt;/p&gt;
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