A note on the average shadowing property for expansive maps (Q649787)
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scientific article; zbMATH DE number 5986536
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on the average shadowing property for expansive maps |
scientific article; zbMATH DE number 5986536 |
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A note on the average shadowing property for expansive maps (English)
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6 December 2011
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This paper proves that, given a compact metric space \(X\) and a continuous map \(f:X\rightarrow X\) with the shadowing property, the following five conditions are equivalent: (1) topological transitivity, (2) weak topological mixing, (3) topological mixing, (4) surjectivity and the specification property, (5) surjectivity and the average shadowing property. The paper includes a thorough discussion on how its results complete and extend existing knowledge. Various corollaries are also presented.
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average shadowing property
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shadowing
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expansive map
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weak mixing
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transitivity
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