Transitivity, two-sided limit shadowing property and dense $omega$-chaos

摘要

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.