Relation of Some Chaos Characterizations on 1-Step Shift of Finite Type over Two Symbols


A collection of sequences over symbols 0 and 1 with specified restrictions constitutes a 1-step shift of finite type over two symbols. A group of prohibited blocks that are not permitted to occur in any sequences within the space serve as a visual cue to the limits. The space is of the finite type since there are a finite number of forbidden blocks, and it is of the 1-step type because the prohibited blocks have a length of 2. The specification property, the virtually specification property, and locally everywhere onto are the three chaotic characterizations that we investigate in this paper for a 1-step shift of finite type across two symbols. We found that, when illustrating the chaotic behaviour of dynamical systems, the specification property and the locally everywhere onto characteristics are more significant than Devaney chaos. However, Devaney chaos is less robust than almost any characteristic.

Author(s) Details:

Malouh Baloush,
Department of Basic Scientific and Human Sciences, National University College of Technology, Jordan.

Syahida Che Dzul-Kifli,
School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia.

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Keywords: Locally everywhere onto, specification property, almost specification property, devaney chaos, shift of finite type

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