A FAMILY OF RANDOM MAPS WHICH POSSES INFINITE ABSOLUTELY CONTINUOUS INVARIANT MEASURES

TitleA FAMILY OF RANDOM MAPS WHICH POSSES INFINITE ABSOLUTELY CONTINUOUS INVARIANT MEASURES
Publication TypeJournal Article
Year of Publication2018
AuthorsISLAM SHAFIQUL
JournalDynamic Systems and Applications
Volume27
Issue4
Start Page729
Pagination14
Date Published09/2018
ISSN1056-2176
AMS Subject Classification37A05, 37H10
Abstract

We consider a family of random maps where each of the component maps is from a family of piecewise, linear and Markov maps on a class of infinite partitions of the state space. We investigate the existence of infinite absolutely continuous invariant measures of the random maps. In a more general setting, our study establishes a positive answer to the question in discrete time dynamical system: can two chaotic systems give rise to order, namely can they be combined into another dynamical system which does not behave chaotically? This question is analogous to Parrondo’s paradox [5] which states that two losing gambling games when combined one after the other (either deterministically or randomly) can result in a winning game: that is, a losing game followed by a losing game = a winning game.
PDFhttps://acadsol.eu/dsa/articles/27/4/3.pdf
DOI10.12732/dsa.v27i4.3
Refereed DesignationRefereed
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