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The Robust Ten Martini Problem
Abstract
We solve the robust ten martini problem: Cantor spectrum with no arithmetic restriction on the irrational frequency for Type I analytic one-frequency quasiperiodic Schrodinger operators. We introduce Type I through a new acceleration-type quantity with stability under analytic perturbations. This yields a global open class of analytic potentials whose associated operators have Cantor spectrum for every irrational frequency.
Related
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BibTeX
@misc{ge2026robust,
title = {{The Robust Ten Martini Problem}},
author = {Lingrui Ge and Svetlana Jitomirskaya and Jiangong You},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15812},
eprint = {2609.15812},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15812},
}
RIS
TY - UNPB
TI - The Robust Ten Martini Problem
AU - Lingrui Ge
AU - Svetlana Jitomirskaya
AU - Jiangong You
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15812
UR - https://arxiv.org/abs/2609.15812
AB - We solve the robust ten martini problem: Cantor spectrum with no arithmetic restriction on the irrational frequency for Type I analytic one-frequency quasiperiodic Schrodinger operators. We introduce Type I through a new acceleration-type quantity with stability under analytic perturbations. This yields a global open class of analytic potentials whose associated operators have Cantor spectrum for every irrational frequency.
ER -