Year: 2015
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Haynes, Alan, Koivusalo, Henna, Walton, James
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G4424468361, G7220250192, G8507742743
OpenAlex ID: W2614036714