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2012/2013 On \(\omega\)-Limit Sets of Triangular Induced Maps
Sergiĭ Kolyada, Damoon Robatian
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Real Anal. Exchange 38(2): 299-316 (2012/2013).


Let \(X\) be a compact topological space and \(T:X\rightarrow X\) a continuous map. Y.N. Dowker, F.G. Friedlander and A.N. Sharkovsky, independently, introduced and studied the notion of \emph{\(T\)-connectedness}. In particular, they showed that any \(\omega\)-limit set of a dynamical system \((X,T)\) is \(T\)-connected. Let \(\big(C(X),F\big)\) be the induced dynamical system of a given system \((X,T)\), where \(C(X)\) is the hyperspace of all compact connected subsets of \(X\) and \(F:C(X)\rightarrow C(X)\) is the induced map of \(T\). In this paper we give a characterization of the induced-map-connected subsets of \(C(I)\), where \(I\) is a compact interval. The characterization is given via the structure of the \(\omega\)-limit sets (located on a fiber) of continuous \emph{triangular induced maps} on \(I\times C(I)\).


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Sergiĭ Kolyada. Damoon Robatian. "On \(\omega\)-Limit Sets of Triangular Induced Maps." Real Anal. Exchange 38 (2) 299 - 316, 2012/2013.


Published: 2012/2013
First available in Project Euclid: 27 June 2014

zbMATH: 1307.37006
MathSciNet: MR3261879

Primary: 26A04 , ‎37B05‎
Secondary: 26A05

Keywords: map-connectedness , omega-limit set , triangular map

Rights: Copyright © 2012 Michigan State University Press

Vol.38 • No. 2 • 2012/2013
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