Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Singular spectrum of Lebesgue measure zero for one-dimensional
  quasicrystals   The spectrum of one-dimensional discrete Schr\"odinger operators associated
to strictly ergodic dynamical systems is shown to coincide with the set of
zeros of the Lyapunov exponent if and only if the Lyapunov exponent exists
uniformly. This is used to obtain Cantor spectrum of zero Lebesgue measure for
all aperiodic subshifts with uniform positive weights. This covers, in
particular, all aperiodic subshifts arising from primitive substitutions
including new examples as e.g. the Rudin-Shapiro substitution.
  Our investigation is not based on trace maps. Instead it relies on an
Oseledec type theorem due to A. Furman and a uniform ergodic theorem due to the
author.

12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
19
The categories of this paper are: eess
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys