On the ranks of an ergodic automorphism \(T\times T\) (Q5951276)
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scientific article; zbMATH DE number 1685372
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the ranks of an ergodic automorphism \(T\times T\) |
scientific article; zbMATH DE number 1685372 |
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On the ranks of an ergodic automorphism \(T\times T\) (English)
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31 October 2002
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The author studies ranks of automorphisms of a Lebesgue space. The main result: Let an automorphism \(T\) be weakly mixing. Then Rank\((T\times T)= \infty\) and \(\beta(T\times T) \leq 1/4\), where \(\beta\) denotes the local rank. Moreover, if \(\beta(T\times T) = 1/4\), then \(T\) is necessarily \(\kappa\)-mixing with \(\kappa=1/2\). This last result confirms an early conjecture by Oseledets.
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automorphism
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rank
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local rank
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weakly mixing
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