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- W3157137214 abstract "In this paper, we derive a sharp condition on the equivalence of topological transitivity among an interval autonomous dynamical system, its induced set-valued system and induced normal fuzzified system. We also prove that their sensitivity (resp., total transitivity) are equivalent. For a general non-autonomous dynamical system, we show the equivalence of topological mixing (resp., mild mixing, cofinite sensitivity, multi-sensitivity and syndetic sensitivity) among the non-autonomous system and its two induced systems. In contrast, we construct a non-autonomous system that is weakly mixing but neither of its two induced systems is weakly mixing. We extend the topological equi-conjugacy between two non-autonomous systems to their two induced systems. Finally, we verify some basic properties of topological entropy among a non-autonomous system and its two induced systems, and establish some sufficient conditions for the topological equi-conjugacy between the fuzzification of a non-autonomous system and a subshift of finite type." @default.
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- W3157137214 date "2021-06-01" @default.
- W3157137214 modified "2023-09-26" @default.
- W3157137214 title "On fuzzifications of non-autonomous dynamical systems" @default.
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- W3157137214 doi "https://doi.org/10.1016/j.topol.2021.107704" @default.
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