Cantor spectrum for the almost Mathieu equation |
| |
Authors: | J Bellissard B Simon |
| |
Institution: | University of Provence and CNRS, Centre de Physique Théorique, Luminy-Case 907, F-13288 Marseille Cedex 09, France;Departments of Mathematics and Physics, California Institute of Technology, Pasadena, California 91125 U.S.A. |
| |
Abstract: | For a dense Gδ of pairs (λ, α) in R2, we prove that the operator (Hu)(n) = u(n + 1) + u(n ?1) + λ cos(2παn + θ) u(n) has a nowhere dense spectrum. Along the way we prove several interesting results about the case of which we mention: (a) If qθ is not an integral multiple of π, then all gaps are open, and (b) If q is even and θ is chosen suitably, then the middle gap is closed for all λ. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|