F-sensitivity and (F_1, F_2)-sensitivity between dynamical systems and their induced hyperspace dynamical systems

Abstract

The notions of F-sensitivity and (F 1 , F 2 )-sensitivity were introduced and studied by Wang et al. via

F-equicontinuity and an Analogue of Auslander-Yorke Dichotomy Theorem

“…Definition 2.2. ( [6], [10][11][12][13][14]) A topological dynamical system (X, T ) is said to be F −sensitive if there exists ε > 0(F −sensitive constant) such that for any nonempty open subset…”

Distributional chaos in a sequence and topologically weak mixing for nonautonomous discrete dynamical systems

“…Chaos of nonautonomous discrete dynamical systems has been extensively studied (see [2,4,6,7,21,25]). For some related concepts and properties for autonomous discrete dynamical systems we refer the reader to [8][9][10][11][12][13][14][15][17][18][19]. A continuous self-map on a metric space is said to be chaotic in the sense of Devaney [1] if it satisfies the following three properties are satisfied: (1) topological transitivity; (2) the denseness of periodic points; (3) sensitive dependence on initial conditions.…”