Positive Hausdorff Dimensional Spectrum for the Critical Almost Mathieu Operator

Bernard Helffer; Qinghui Liu; Yanhui Qu; Qi Zhou

doi:10.1007/s00220-018-3278-6

Positive Hausdorff Dimensional Spectrum for the Critical Almost Mathieu Operator

Bernard Helffer
, Qinghui Liu
, Yanhui Qu^*
, Qi Zhou

^*Corresponding author for this work

School of Mathematics and Statistics

Laboratoire de Mathématiques Jean Leray
Université Paris-Saclay
Tsinghua University
Nanjing University

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	369-382
Number of pages	14
Journal	Communications in Mathematical Physics
Volume	368
Issue number	1
DOIs	https://doi.org/10.1007/s00220-018-3278-6
Publication status	Published - 1 May 2019

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title = "Positive Hausdorff Dimensional Spectrum for the Critical Almost Mathieu Operator",

abstract = "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.",

author = "Bernard Helffer and Qinghui Liu and Yanhui Qu and Qi Zhou",

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AU - Liu, Qinghui

AU - Qu, Yanhui

AU - Zhou, Qi

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N2 - 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.

AB - 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.

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JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

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Positive Hausdorff Dimensional Spectrum for the Critical Almost Mathieu Operator

Abstract

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