Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral Properties of Limit-Periodic Schr\"odinger Operators   We investigate the spectral properties of Schr\"odinger operators in l^2(Z)
with limit-periodic potentials. The perspective we take was recently proposed
by Avila and is based on regarding such potentials as generated by continuous
sampling along the orbits of a minimal translation of a Cantor group. This
point of view allows one to separate the base dynamics and the sampling
function. We show that for any such base dynamics, the spectrum is a Cantor set
of positive Lebesgue measure and purely absolutely continuous for a dense set
of sampling functions, and it is a Cantor set of zero Lebesgue measure and
purely singular continuous for a dense G_\delta set of sampling functions.

34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat