Transitivity, two-sided limit shadowing property and dense \(\omega\)-chaos (Q2877786)
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scientific article; zbMATH DE number 6334130
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Transitivity, two-sided limit shadowing property and dense \(\omega\)-chaos |
scientific article; zbMATH DE number 6334130 |
Statements
25 August 2014
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shadowing property
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limit shadowing
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pseudo-orbit
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asymptotic tracing
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minimal set
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\(\omega\)-chaos
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topological graph
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Transitivity, two-sided limit shadowing property and dense \(\omega\)-chaos (English)
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This paper studies \(\omega\)-chaos and two-sided limit shadowing property (TSLmSP). The author starts with several results in the spirit of Smale-Bowen spectral decomposition characterizing dynamical properties of maps with the TSLmSP. Next, it is proven that a transitive nonminimal dynamical system with the TSLmSP has a c-dense \(\omega\)-scrambled set. Finally, it is proven that a transitive dynamical system on a topological graph that is not an irrational rotation always has a dense Mycielski \(\omega\)-chaotic set.
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