Abstract
We introduce two new characterizations of Meyer sets. A repetitive Delone set in ℝd of finite local complexity is topologically conjugate to a Meyer set if and only if it has d linearly independent topological eigenvalues, which is if and only if it is topologically conjugate to a bundle over a d-torus with totally disconnected compact fiber and expansive canonical action. ‘Conjugate to’ is a non-trivial condition, as we show that there exist sets that are topologically conjugate to Meyer sets but are not themselves Meyer. We also exhibit a diffractive set that is not Meyer, answering in the negative a question posed by Lagarias, and exhibit a Meyer set for which the measurable and topological eigenvalues are different.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
