Tiling Spaces, Codimension One Attractors and Shape

Details Tiling Spaces, Codimension One Attractors and Shape Tiling Spaces, Codimension One Attractors and Shape

2011-05-04

arxiv.org/abs/1105.0835v1

Mathematics

Dynamical Systems

Scientific paper

We show that any codimension one hyperbolic attractor of a di?eomorphism of a (d+1)-dimensional closed manifold is shape equivalent to a (d+1)-dimensional torus with a ?nite number of points removed, or, in the non-orientable case, to a space with a 2 to 1 covering by such a torus-less-points. Furthermore, we show that each orientable attractor is homeomorphic to a tiling space associated to an aperiodic tiling of Rd, but that the converse is generally not true. This work allows the de?nition of a new invariant for aperiodic tilings, in many cases ?ner than the cohomological or K-theoretic invariants studied to date.

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