The Z^d Alpern multi-tower theorem for rectangles: a tiling approach

Details The Z^d Alpern multi-tower theorem for rectangles: a tiling approach The Z^d Alpern multi-tower theorem for rectangles: a tiling approach

2008-01-18

arxiv.org/abs/0801.2958v1

Mathematics

Dynamical Systems

14 pages, 3 figures

Scientific paper

We provide a proof of the Alpern multi-tower theorem for Z^d actions. We reformulate the theorem as a problem of measurably tiling orbits of a Z^d action by a collection of rectangles whose corresponding sides have no non-trivial common divisors. We associate to such a collection of rectangles a special family of generalized domino tilings. We then identify an intrinsic dynamic property of these tilings, viewed as symbolic dynamical systems, which allows for a multi-tower decomposition.

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