The topological structure of attractors for differentiable functions (Q1912721)

A cleavage between the structure of \(\omega\)-limit sets for continuous functions and the structure of \(\omega\)-limit sets for Lipschitz functions described in \textit{A. M. Bruckner} and \textit{T. H. Steele} [J. Math. Anal. Appl. 188, No. 3, 798-808 (1994; Zbl 0820.26001)] rested on measure theoretic considerations. Present paper shows that the situation is different when the topological structure of these classes of \(\omega\)-limit sets is considered. It is shown that every nowhere dense compact set is homeomorphic to an \(\omega\)-limit set for a differentiable function with bounded derivative.