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Cantor Spectrum via a Reducibility-Duality Bridge for the Mosaic Almost Mathieu Operator
Abstract
We study the mosaic Almost Mathieu operator, a quasiperiodic model that naturally admits a singular strip-Jacobi representation. By establishing a duality framework and extending the correspondence between the integrated density of states and the fibered rotation number to this setting, we obtain an effective reduction to SL(2,ℝ) cocycles. As a consequence, combining Aubry duality, reducibility theory, and the Moser--Pöschel argument, we prove that the spectrum is a Cantor set for all noncritical parameters.
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BibTeX
@misc{he2026cantor,
title = {{Cantor Spectrum via a Reducibility-Duality Bridge for the Mosaic Almost Mathieu Operator}},
author = {Jiawei He and Yuan Shan and Yongjian Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.23422},
eprint = {2606.23422},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.23422},
}
RIS
TY - UNPB
TI - Cantor Spectrum via a Reducibility-Duality Bridge for the Mosaic Almost Mathieu Operator
AU - Jiawei He
AU - Yuan Shan
AU - Yongjian Wang
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2606.23422
UR - https://arxiv.org/abs/2606.23422
AB - We study the mosaic Almost Mathieu operator, a quasiperiodic model that naturally admits a singular strip-Jacobi representation. By establishing a duality framework and extending the correspondence between the integrated density of states and the fibered rotation number to this setting, we obtain an effective reduction to SL(2,ℝ) cocycles. As a consequence, combining Aubry duality, reducibility theory, and the Moser--Pöschel argument, we prove that the spectrum is a Cantor set for all noncritical parameters.
ER -