Equivalence classes of codimension one cut-and-project sets

TY - JOUR

T1 - Equivalence classes of codimension one cut-and-project sets

AU - Haynes, Alan

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

U2 - 10.1017/etds.2014.90

DO - 10.1017/etds.2014.90

M3 - Article

SN - 0143-3857

VL - 36

SP - 816

EP - 831

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

IS - 3

ER -