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The Rotation Number for Almost Periodic Schrödinger Operators with \(\delta \)-Potentials

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Abstract

We consider one-dimensional Schrödinger operators with almost periodic potentials and \(\delta \)-interactions supported on an almost periodic point set and with almost periodic coefficients. For operators of this kind we introduce a rotation number in the spirit of Johnson and Moser.

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Acknowledgements

Z. Z. would like to express his gratitude to Prof. Meirong Zhang for helpful suggestions. Z. Z. also thanks Department of Mathematics at Rice University for their warm hospitality when he visited Prof. David Damanik. Some part of this paper was done during the visit to the department. We would like to express our sincere thanks to the anonymous referees for helpful comments.

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Authors and Affiliations

  1. Department of Mathematics, Rice University, Houston, TX, 77005, USA

    David Damanik

  2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Zhe Zhou

  3. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    Zhe Zhou

Authors
  1. David Damanik
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  2. Zhe Zhou
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Corresponding author

Correspondence to Zhe Zhou.

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Dedicated to the memory of Russell Johnson.

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D. D. was supported in part by NSF Grant DMS–1700131 and by an Alexander von Humboldt Foundation research award. Z. Z. was supported in part by the National Natural Science Foundation of China (Grant No. 12090014)

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Damanik, D., Zhou, Z. The Rotation Number for Almost Periodic Schrödinger Operators with \(\delta \)-Potentials. J Dyn Diff Equat 34, 155–177 (2022). https://doi.org/10.1007/s10884-021-10019-z

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  • DOI: https://doi.org/10.1007/s10884-021-10019-z

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