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arXiv · 2606.23422

Cantor Spectrum via a Reducibility-Duality Bridge for the Mosaic Almost Mathieu Operator

Jiawei He·Yuan Shan·Yongjian Wang
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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 $SL(2,\mathbb{R})$ cocycles. As a consequence, combining Aubry duality, reducibility theory, and the Moser--P\"oschel argument, we prove that the spectrum is a Cantor set for all noncritical parameters.

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Jiawei He, Yuan Shan, Yongjian Wang. 2026-06-22. Cantor Spectrum via a Reducibility-Duality Bridge for the Mosaic Almost Mathieu Operator. https://arxiv.org/abs/2606.23422

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