TITLE: Cantor Spectrum for quasi-periodic Schr\"odinger Operators

AUTHOR: Joaquim Puig. Departament de Matem\`atica Aplicada i
An\`alisi, Univ. de Barcelona, Gran Via 585, 08007 Barcelona, Spain.
puig@maia.ub.es

ABSTRACT: We present some results concerning the Cantor structure of
the spectrum of quasi-periodic Schr\"odinger operators. These are obtained
studying the dynamics of the corresponding eigenvalue equations, specially
the notion of reducibility and Floquet theory. We will deal with the
Almost Mathieu case, and the solution of the ``Ten Martini Problem'' for
Diophantine frequencies, as well as other models.


