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

Piotr Oprocha
대한수학회 (The Korean Mathematical Society)|2014.07|대한수학회지 (Journal of the KMS)|제51권 제4호|pp. 837-851

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참고문헌

키워드

limit shadowingshadowing propertyminimal setpseudo-orbitasymptotic tracingω-chaostopological graph.
주제분류수학

초록

We consider ω-chaos as defined by S. H. Li in 1993. We show that c-dense ω-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 ω-scrambled set. As a preliminary step, we provide a characterization of dynamical properties of maps with TSLmSP.

Abstract

We consider ω-chaos as defined by S. H. Li in 1993. We show that c-dense ω-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 ω-scrambled set. As a preliminary step, we provide a characterization of dynamical properties of maps with TSLmSP.

참고문헌 (29)

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