Non-transitive points and porosity (Q2866750)
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scientific article; zbMATH DE number 6238577
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Non-transitive points and porosity |
scientific article; zbMATH DE number 6238577 |
Statements
Non-transitive points and porosity (English)
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16 December 2013
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porosity and \(\sigma \)-porosity
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transitivity
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subshifts
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interval map
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Lipschitz and Hölder continuity
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recurrence
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proximality
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From the author's summary: ``We establish that for a fairly general class of topologically transitive dynamical systems, the set of non-transitive points is very small when the rate of transitivity is very high. The notion of smallness that we consider here is that of \(\sigma\)-porosity.''NEWLINENEWLINE The author proves that the set of non-transitive points is \(\sigma\)-porous for any subshift, a result that extends to some finite-to-one factor systems.
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