Band invariants and closed trajectories on \(S^ n\)
type: Item
instance of: scholarly article
title: Band invariants and closed trajectories on \(S^ n\)
zbMATH Open document ID: 0587.58049
DOI: 10.1016/0001-8708(85)90120-3
author: A. Uribe
published in: Advances in Mathematics
publication date: 1985-01-01T00:00:00Z
review text: The author considers the spectral properties of the Schrödinger operator \(\Delta +g\) where \(\Delta\) is the Laplace-Beltrami operator on \(S^ n\) and \(g\in C^{\infty}(S^ n)\) is a given potential. The spectrum of \(\Delta +g\) forms bands of fixed width around the spectrum of the Laplace-Beltrami operator. It is shown that, under certain conditions on g, there is a correspondence between clustering in the bands and the existence of closed classical orbits, i.e. integral curves of the Hamiltonian \(| p|^ 2+g\) on \(T^*S^ n\). The author also relates the asymptotic behavior of the periods of the trajectories to the spectrum of \(\Delta +g\).
Mathematics Subject Classification ID: 58J50
Mathematics Subject Classification ID: 35P20
Mathematics Subject Classification ID: 81P99
Mathematics Subject Classification ID: 37J99
zbMATH DE Number: 3942574
zbMATH Keywords: Laplace-Beltrami-Schrödinger operator
zbMATH Keywords: spectral analysis
zbMATH Keywords: correspondence principle
MaRDI profile type: Publication
full work available at URL: 0001-8708(85)90120-3
OpenAlex ID: W2058455192
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description: scientific article; zbMATH DE number 3942574