TITLE:
The spectrum of Schr\"odinger operators with quasi-periodic potential:
a dynamical approach

AUTHORS:
Joaquim Puig  and Carles Sim\'o

Departament de Matem\`atica Aplicada i An\`alisi, Universitat de Barcelona,
Gran Via 585, 08007 Barcelona (Spain)

ABSTRACT:
Some results on the spectrum of Schr\"odinger operators with quasi-periodic
real analytic potential and Diophantine frequencies are presented. The
eigenvalue equation associated to this operator is a quasi-periodic
generalization of Hill's equation with periodic forcing. A dynamical study
of this equation allows an accurate description of the structure of stability
zones close to constant coefficients. This study has direct applications to
the structure of the spectrum of Schr\"odinger operators with small quasi-
periodic forcing. In particular we discuss the occurrence of Cantor spectrum.