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PreprintCC BY 4.0arXiv

On the types of quasiperiodic potentials and level surfaces of quasiperiodic functions

  • A. Ya. Maltsev
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Abstract

We examine the similarities and differences between two types of quasiperiodic functions: those obtained by restricting smooth periodic functions in ℝN to lower-dimensional subspaces ℝn ⊂ ℝN, and those that arise as physical fields or potentials in quasicrystalline structures. Our analysis reveals that functions in these two classes share a number of common features while also exhibiting significant differences. As a key tool for investigating both classes of functions, we employ the Novikov problem - specifically, the problem of describing the global geometry of the level sets of quasiperiodic functions.

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Cite

BibTeXRIS
BibTeX
@misc{maltsev2026types,
  title = {{On the types of quasiperiodic potentials and level surfaces of quasiperiodic functions}},
  author = {A. Ya. Maltsev},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.34989},
  eprint = {2610.34989},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.34989},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On the types of quasiperiodic potentials and level surfaces of quasiperiodic functions
AU  - A. Ya. Maltsev
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.34989
UR  - https://arxiv.org/abs/2610.34989
AB  - We examine the similarities and differences between two types of quasiperiodic functions: those obtained by restricting smooth periodic functions in ℝ^N to lower-dimensional subspaces ℝ^n ⊂ ℝ^N, and those that arise as physical fields or potentials in quasicrystalline structures. Our analysis reveals that functions in these two classes share a number of common features while also exhibiting significant differences. As a key tool for investigating both classes of functions, we employ the Novikov problem - specifically, the problem of describing the global geometry of the level sets of quasiperiodic functions.
ER  -