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 (f) over bar : K(X) -> K(X) be defined by (f) over bar (A) = {f(a)/a is an element of A} the natural extension of f to K(X), then the aim of this work is to study the dynamics of (f) over bar when f is turbulent (erratic, respectively) and its relationships.

Keywords

Chaos, dynamical systems, turbulent functions, erratic functions

Language

English

Citation

Proceedings Of The Joint 2009 International Fuzzy Systems Association World Congress And 2009 European Society Of Fuzzy Logic And Technology Conference. Linz: European Soc Fuzzy Logic & Technology, p. 231-233, 2009.