Projects per year
Abstract
We establish a connection between gaps problems in Diophantine approximation and the frequency spectrum of patches in cut and project sets with special windows. Our theorems provide bounds for the number of distinct frequencies of patches of size r, which depend on the precise cut and project sets being used, and which are almost always less than a power of log r. Furthermore, for a substantial collection of cut and project sets we show that the number of frequencies of patches of size r remains bounded as r tends to infinity. The latter result applies to a collection of cut and project sets of full Hausdorff dimension.
Original language  English 

Pages (fromto)  6585 
Journal  Mathematical Proceedings of the Cambridge Philosophical Society 
Volume  161 
Issue number  1 
Early online date  3 Mar 2016 
DOIs  
Publication status  Published  Jul 2016 
Projects
 2 Finished

Diophantine approximation, chromatic number, and equivalence classes of separated nets
10/10/13 → 9/07/15
Project: Research project (funded) › Research

Career Acceleration Fellowship: Circle rotations and their generalisation in Diophantine approximation
1/10/13 → 30/09/16
Project: Research project (funded) › Research