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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.06918 |
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Table of Contents:
- This paper solves ``The Dry Ten Martini Problem'' for $C^2$ cosine-type quasiperiodic Schrödinger operators with large coupling constants and Diophantine frequencies, a model originally introduced by Sinai in 1987 \cite{sinai}. This shows that the analyticity assumption on the potential is not essential for obtaining a dry Cantor spectrum and can be replaced by a certain geometric condition in the low regularity case. In addition, we prove the homogeneity of the spectrum and the absolute continuity of the integrated density of states (IDS).