Equicontinuous delone dynamical systems

D. Lenz; Johannes Kellendonk (ICJ)

Equicontinuous delone dynamical systems

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1105.3855 v1 pith:LI4TXBJE submitted 2011-05-19 math.DS

Johannes Kellendonk (ICJ) , D. Lenz This is my paper · ORCID

classification math.DS

keywords delonesystemsequicontinuouscrystallinedynamicalalmostclasscomplexity

verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments

read the original abstract

We characterize equicontinuous Delone dynamical systems as those coming from Delone sets with strongly almost periodic Dirac combs. Within the class of systems with nite local complexity the only equicontinuous systems are then shown to be the crystalline ones. On the other hand, within the class without nite local complexity, we exhibit examples of equicontinuous minimal Delone dynamical systems which are not crystalline. Our results solve the problem posed by Lagarias whether a Delone set whose Dirac comb is strongly almost periodic must be crystalline.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Pure point measures with sparse support and sparse Fourier--Bohr support
math.MG 2019-08 accept novelty 7.0 of 10

Doubly sparse measures on second countable locally compact Abelian groups are shown to be supported on finitely many translates of a lattice with trigonometric polynomial amplitudes.

Pith tools