English

Zero Hausdorff dimension spectrum for the almost Mathieu operator

Mathematical Physics 2016-05-25 v2 math.MP Spectral Theory

Abstract

We study the almost Mathieu operator at critical coupling. We prove that there exists a dense GδG_\delta set of frequencies for which the spectrum is of zero Hausdorff dimension.

Cite

@article{arxiv.1510.07651,
  title  = {Zero Hausdorff dimension spectrum for the almost Mathieu operator},
  author = {Yoram Last and Mira Shamis},
  journal= {arXiv preprint arXiv:1510.07651},
  year   = {2016}
}

Comments

v1: 24 pp. v2: 25 pp, corrected the statement of Theorem 3 and added explanations in the proof of Theorem 2

R2 v1 2026-06-22T11:29:22.772Z