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Chaos, entropy and a generalized extension principle. (English) Zbl 0827.58037

Summary: We show a relationship between a very simple criterion, positive topological entropy and Li-Yorke chaos. A general definition of fuzzification and level set, based on \(t\)-norms/conorms and their diagonal functions, is introduced. The chaos theorem of Benhabib and Day for set valued mappings is considerably strengthened and generalised.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
54C70 Entropy in general topology
03E72 Theory of fuzzy sets, etc.
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