Connections between universal observability and topological dynamics (Q5931753)
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scientific article; zbMATH DE number 1591746
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Connections between universal observability and topological dynamics |
scientific article; zbMATH DE number 1591746 |
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Connections between universal observability and topological dynamics (English)
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25 April 2001
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uniform observability
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topological dynamics
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real flow
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primality
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minimality
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distality
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nonasymptoticality
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almost one-to-one quotient
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0.88763356
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0.8793648
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0.8739575
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The author gives results relating topological properties of real flows \(\varphi\) on compact Hausdorff spaces to universal observability, i.e., to the fact that for any nonconstant function \(f\) the implication \(f(\varphi(t,x))=f(\varphi(t,y))\) for all \(t\geq 0\) \(\Rightarrow\) \(x=y\) holds. NEWLINENEWLINENEWLINEIn an earlier paper by the author [Proc. MTNS98, A. Beghi, L. Finesso, G. Picci (eds.), Il Poligrafo, Padova, Italy, 133-136 (1998)] it was shown that universal observability is equivalent to the flow being prime and having positively separated quotients. NEWLINENEWLINENEWLINEIn the paper under review first the proof of this result is simplified and then universal observability is related to a couple of other topological properties of the flow like minimality, nonasymptoticality, distality, and the existence of almost one-to-one quotients.
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