On fuzzifications of non-autonomous dynamical systems

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

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Original languageEnglish
Article number107704
Journal / PublicationTopology and its Applications
Online published27 Apr 2021
Publication statusPublished - 15 Jun 2021


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.

Research Area(s)

  • Fuzzy set, Mixing, Non-autonomous dynamical system, Sensitivity, Topological equi-conjugacy