Topological ergodic decompositions and applications to products of powers of a minimal transformation |
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Authors: | Eli Glasner |
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Affiliation: | 1. School of Mathematics, Tel Aviv University, Ramat Aviv, Israel
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Abstract: | For a minimal distal flow (X, T) and a positive integern, let be the largest distal factor of ordern. The existence of a denseG δ subset ω ofX is shown, such that forx ∈ ω the orbit closure of (x,x,...,x) ∈ X n+1 under τ =T ×T 2 ... ×T n+1 is π-saturated. In fact, an analogous statement for a general minimal flow is proved in terms of its PI-tower. On the way we get some topological “ergodic” decomposition theorems. |
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