Orbit Tracing Properties on Hyperspaces and Fuzzy Dynamical Systems

Let X be a compact metric space and continuous map f:X→X which defines discrete dynamical system (X,f). The f induces two natural maps, namely f¯:K(X)→K(X) on the hyperspace K(X) of non-empty subspaces Zadeh’s extension f^:F(X)→F(X) F(X) normal fuzzy set. In this work, we analyze interaction some orbit tracing properties, specification shadowing properties (X,f) its induced systems (K(X),f¯) (F(X),f^). Adding an algebraic structure yields stronger conclusions, obtain full characterization property in hyperspace, space, phase if assume that later is convex subset (metrizable complete) locally linear operator.