POSITIVE HAUSDORFF DIMENSIONAL SPECTRUM FOR THE CRITICAL ALMOST MATHIEU OPERATOR

Bernard Helffer (1) , Qinghui Liu (2) , Yanhui Qu (3) , Qi Zhou (4)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 BIT - Beijing Institute of Technology
3 THU - Tsinghua University [Beijing]
4 NJU - Nanjing University

We show that there exists a dense set of frequencies with positive Hausdorff dimension for which the Hausdorff dimension of the spectrum of the critical almost Mathieu operator is positive.

Domaines: Physique mathématique [math-ph]

Bernard Helffer, Qinghui Liu, Yanhui Qu, Qi Zhou. POSITIVE HAUSDORFF DIMENSIONAL SPECTRUM FOR THE CRITICAL ALMOST MATHIEU OPERATOR. Communications in Mathematical Physics, In press. ⟨hal-01875416⟩