English

The rotation number for almost periodic potentials with jump discontinuities and $\delta$-interactions

Dynamical Systems 2023-12-12 v2 Classical Analysis and ODEs

Abstract

We consider one-dimensional Schr\"odinger operators with generalized almost periodic potentials with jump discontinuities and δ\delta-interactions. For operators of this kind we introduce a rotation number in the spirit of Johnson and Moser. To do this, we introduce the concept of almost periodicity at a rather general level, and then the almost periodic function with jump discontinuities and δ\delta-interactions as an application.

Keywords

Cite

@article{arxiv.2112.00372,
  title  = {The rotation number for almost periodic potentials with jump discontinuities and $\delta$-interactions},
  author = {David Damanik and Meirong Zhang and Zhe Zhou},
  journal= {arXiv preprint arXiv:2112.00372},
  year   = {2023}
}

Comments

34 pages, to appear in Annales Henri Poincar\'e