Chaos induced by turbulent and erratic functions - Roman-Flores, H.; Chalco-Cano, Y.; Nunes-Silva, G. [UNESP] (My University, 2009)
Let (X, d) be a compact metric space and f: X → X a continuous function and consider the hyperspace (K(X), H) of all nonempty compact subsets of X endowed with the Hausdorff metric induced by d. Let f̄: K(X) → K (X) be defined by f̄(A) = {f(a)/a ∈ A} the natural extension of f to K(X), then the aim of this work is to study the dynamics of f when f is turbulent (erratic, respectively) and its relationships.
Keywords: Chaos; Dynamical systems; Erratic functions; Turbulent functions; Compact metric spaces; Compact subsets; Continuous functions; Hausdorff metric; Natural extension; Chaos theory; Fuzzy systems; Fuzzy logic