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- W2950967090 abstract "Rudolph showed that the orbits of any measurable, measure preserving $mathbb R^d$ action can be measurably tiled by $2^d$ rectangles and asked if this number of tiles is optimal for $d>1$. In this paper, using a tiling of $mathbb R^d$ by notched cubes, we show that $d+1$ tiles suffice. Furthermore, using a detailed analysis of the set of invariant measures on tilings of $mathbb R^2$ by two rectangles, we show that while for $mathbb R^2$ actions with completely positive entropy this bound is optimal there exist mixing $mathbb R^2$ actions whose orbits can be tiled by 2 tiles." @default.
- W2950967090 created "2019-06-27" @default.
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- W2950967090 date "2012-10-18" @default.
- W2950967090 modified "2023-10-18" @default.
- W2950967090 title "Rudolph's Two-Step Coding Theorem and Alpern's Lemma for R^d Actions" @default.
- W2950967090 hasPublicationYear "2012" @default.
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