Journal of the
Korean Mathematical Society JKMS

We consider $\omega$-chaos as defined by S. H. Li in 1993. We show that c-dense $\omega$-scrambled sets are present in every transitive system with two-sided limit shadowing property (TSLmSP) and that every transitive map on topological graph has a dense Mycielski $\omega$-scrambled set. As a preliminary step, we provide a characterization of dynamical properties of maps with TSLmSP.

Keywords: shadowing property, limit shadowing, pseudo-orbit, asymptotic tracing, minimal set, $\omega$-chaos, topological graph

MSC numbers: Primary 37B05; Secondary 37C50, 37B20