Ergodicity in affine skew product toral extensions (Q760524)
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scientific article; zbMATH DE number 3884423
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Ergodicity in affine skew product toral extensions |
scientific article; zbMATH DE number 3884423 |
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Ergodicity in affine skew product toral extensions (English)
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1986
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We examine the dynamics of those skew product extensions in which the fibre is a torus supporting a group of automorphisms which intertwine with the given \({\mathbb{Z}}^ n\) action. The main results concern lifting ergodicity generically from the base when the original action is perturbed into a new action by a continuous affine cocycle. Extensions are indicated for other properties, such as weak-mixing and Bernoulli, and smooth variants are stated.
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skew product extensions
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torus supporting a group of automorphisms
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lifting ergodicity
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continuous affine cocycle
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weak-mixing
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Bernoulli
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