Asymptotic properties of multifunctions, families of measures and Markov operators associated with cocycles. (January 2016)

• Record Type: Journal Article
• Authors: Guzik, Grzegorz
• Is Part Of: Nonlinear analysis. Volume 130(2015)
• Page Start: 59
• Page End: 75
• Publication Date: 2016-01
• Subjects: primary 28A80 54H20 -- secondary 26E25 47H04 93E03; Asymptotic stability and semistability -- Attractor -- Nonautonomous/random dynamical system -- Cocycle -- Attracting measure -- Markov operator; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.09.024
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider asymptotic properties of families of multifunctions generated by cocycles, families of measures as well as Markov operators associated with such a mapping. The results we apply to random dynamical systems show connection of obtained attractors for families of multifunctions with global set attractors and also connection of supports of attracting measures for Markov families with global point attractors. The use of topological limits instead of standard Hausdorff distance lets us to get attractors under some quite general assumptions only on a cocycle mapping but without any assumptions on so-called parameter space and without standard assumption on existence of a compact absorbing set.