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

Title & Authors
TRANSITIVITY, TWO-SIDED LIMIT SHADOWING PROPERTY AND DENSE ω-CHAOS
Oprocha, Piotr;

Abstract
We consider $\small{{\omega}}$-chaos as defined by S. H. Li in 1993. We show that c-dense $\small{{\omega}}$-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 $\small{{\omega}}$-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;$\small{{\omega}}$-chaos;topological graph;
Language
English
Cited by
1.
The limit shadowing property and Li–Yorke’s chaos, Asian-European Journal of Mathematics, 2016, 09, 01, 1650007
2.
Limit Sets, Attractors and Chaos, Qualitative Theory of Dynamical Systems, 2017, 16, 1, 53
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