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Abstract. We prove some results concerning the entropy of Darboux (and almost continuous) functions. We first generalize some theorems valid for continuous functions, and then we study properties which are specific to Darboux functions. Finally, we give theorems on approximating almost continuous functions by functions with infinite entropy.

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The connection between transitivity and existence of a dense orbit for multifunctions φ : X X in generalized topological spaces is studied. Moreover strongly transitive multifunctions and functions in generalized topological spaces are investigated.

In the paper, we examine local aspects of chaos for self-functions on topological manifolds. For this purpose, issues related to focal entropy points and homoclinic points are used. We consider also distortion of dynamical systems which is a theoretical analogue to wave interference.