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Topological ergodic decompositions and applications to products of powers of a minimal transformation

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Abstract

For a minimal distal flow (X, T) and a positive integern, let\(X\xrightarrow{\pi }Y\) 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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Correspondence to Eli Glasner.

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Glasner, E. Topological ergodic decompositions and applications to products of powers of a minimal transformation. J. Anal. Math. 64, 241 (1994). https://doi.org/10.1007/BF03008411

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Keywords

  • Periodic Point
  • Orbit Closure
  • Minimal Flow
  • Topological Dynamic
  • Characteristic Factor