F-sensitivity and multi-sensitivity of hyperspatial dynamical systems

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

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Detail(s)

Original languageEnglish
Pages (from-to)16-26
Journal / PublicationJournal of Mathematical Analysis and Applications
Volume429
Issue number1
Online published7 Apr 2015
Publication statusPublished - 1 Sep 2015

Abstract

Let f be a continuous self-map defined on a compact metric space X and f be a continuous self-map naturally induced by f on the hyperspace K(X) of all nonempty compact subsets of X endowed with a Hausdorff metric. Firstly, a few sufficient and necessary conditions to ensure a dynamical system be F-sensitive or multi-sensitive are obtained. Then, the following results are proved:. (1)If (X,f) is a non-minimal M-system, then (K(X),f) has Fs-sensitive pairs almost everywhere.(2)If (K(X),f) or (K(Y),g) is F-sensitive, then (K(X×Y),f×g) is F-sensitive.(3)(K(X×Y),f×g) is multi-sensitive if and only if (K(X),f) or (K(Y),g) is multi-sensitive, if and only if (X,f) or (Y,g) is multi-sensitive. Moreover, it is proved that f× g is multi-sensitive if and only if f or g is multi-sensitive. This is a positive answer to a question posed in R. Li and X. Zhou (2013) [18].

Research Area(s)

  • F-sensitivity, Furstenberg family, Hyperspace, Multi-sensitivity, Product dynamical system