, Volume 84, Issue 3, pp 403-438

The rotation number for almost periodic potentials

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Abstract

We define and analyze the rotation number for the almost periodic Schrödinger operatorL= −d 2/dx 2+q(x). We use the rotation number to discuss (i) the spectrum ofL; (ii) its relation to the Korteweg-de Vries equation.

Partially supported by the National Science Foundation under Grant NSF-MCS 77-01986
Communicated by A. Jaffe