Chaos induced by turbulent and erratic functions

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.

Palavras-chave

Chaos , Dynamical systems , Erratic functions , Turbulent functions , Compact metric spaces , Compact subsets , Continuous functions , Hausdorff metric , Natural extension , Chaos theory , Fuzzy systems , Fuzzy logic

Idioma

Inglês

Citação

2009 International Fuzzy Systems Association World Congress and 2009 European Society for Fuzzy Logic and Technology Conference, IFSA-EUSFLAT 2009 - Proceedings, p. 231-233.