Equivalence classes of codimension one cut-and-project sets

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We prove that in any totally irrational cut-and-project setup with codimension (internal space dimension) one, it is possible to choose sections (windows) in non-trivial ways so that the resulting sets are bounded displacement equivalent to lattices. Our proof demonstrates that for any irrational α, regardless of Diophantine type, there is a collection of intervals in R/Z which is closed under translation, contains intervals of arbitrarily small length, and along which the discrepancy of the sequence {nα} is bounded above uniformly by a constant.
Original languageEnglish
Pages (from-to)816-831
Number of pages16
JournalErgodic Theory and Dynamical Systems
Issue number3
Early online date11 Nov 2014
Publication statusPublished - 2015

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