It is observed that IFSs are defined based on the concept that the iterates take only an integer number of times. This work studies the dynamics of functions, where a function can iterate r times for every r ∈ R. Utilizing concepts from fuzzy sets, r-times iterates of a function are defined for r ∈ R. The study demonstrates that the chaotic property can be generalized to this new iterative concept. The chaotic behavior of a function is then extended using this iterative concept.
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Selvy et al. (2024) studied this question.
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