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Rigidity in topological dynamics. (English) Zbl 0661.58027
In analogy with the ergodic theoretical notion, we introduce notions of rigidity for a minimal flow (X,T) according to the various ways a sequence $$T^{n_ i}$$ can tend to the identity transformation. The main results obtained are: (i) On a rigid flow there exists a T-invariant, symmetric, closed relation $$\bar N$$ such that (X,T) is uniformly rigid iff $$\bar N=\Delta$$, the diagonal relation. (ii) For syndetically distal (hence distal) flows rigidity is equivalent to uniform rigidity. (iii) We construct a family of rigid flows which includes Körner’s example, in which $$\bar N$$ exhibits kinds of behaviour, e.g. $$\bar N$$ need not be an equivalence relation. (iv) The structure of flows in the above mentioned family is investigated. It is shown that these flows are almost automorphic.
Reviewer: S.Glasner

##### MSC:
 37C10 Dynamics induced by flows and semiflows
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##### References:
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