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- W2079119511 abstract "We give an application of a topological dynamics version of multidimensional Brown’s lemma to tiling theory: given a tiling of an Euclidean space and a finite geometric pattern of points $$F$$ , one can find a patch such that, for each scale factor $$lambda $$ , there is a vector $$vec {t}_lambda $$ so that copies of this patch appear in the tilling “nearly” centered on $$lambda F+vec {t}_lambda $$ once we allow “bounded perturbations” in the structure of the homothetic copies of $$F$$ . Furthermore, we introduce a new unifying setting for the study of tiling spaces which allows rather general group “actions” on patches and we discuss the local isomorphism property of tilings within this setting." @default.
- W2079119511 created "2016-06-24" @default.
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- W2079119511 date "2013-03-21" @default.
- W2079119511 modified "2023-09-27" @default.
- W2079119511 title "Metrics on tiling spaces, local isomorphism and an application of Brown’s lemma" @default.
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- W2079119511 doi "https://doi.org/10.1007/s00605-013-0484-3" @default.
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