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TRANSITIVITY, TWO-SIDED LIMIT SHADOWING PROPERTY AND DENSE ω-CHAOS

  • Oprocha, Piotr (AGH University of Science and Technology Faculty of Applied Mathematics, Institute of Mathematics Polish Academy of Sciences)
  • Received : 2013.12.14
  • Published : 2014.07.01

Abstract

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

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