Linear repetitivity and subadditive ergodic theorems for cut and project sets

TY - UNPB

T1 - Linear repetitivity and subadditive ergodic theorems for cut and project sets

AU - Haynes, Alan

AU - Koivusalo, Henna Lotta Louisa

AU - Walton, Jamie

PY - 2015

Y1 - 2015

N2 - By using a combination of algebraic, geometric, and dynamical techniques, together with input from higher dimensional Diophantine approximation, we give a complete characterization of all linearly repetitive cut and project sets with cubical windows. We also prove that these are precisely the collection of such sets which satisfy subadditive ergodic theorems. The results are explicit enough to allow us to apply them to known classical models, and to construct linearly repetitive cut and project sets in all pairs of dimensions and codimensions in which they exist.

AB - By using a combination of algebraic, geometric, and dynamical techniques, together with input from higher dimensional Diophantine approximation, we give a complete characterization of all linearly repetitive cut and project sets with cubical windows. We also prove that these are precisely the collection of such sets which satisfy subadditive ergodic theorems. The results are explicit enough to allow us to apply them to known classical models, and to construct linearly repetitive cut and project sets in all pairs of dimensions and codimensions in which they exist.

M3 - Preprint

BT - Linear repetitivity and subadditive ergodic theorems for cut and project sets

ER -