Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Zero measure Cantor spectra for continuum one-dimensional quasicrystals   We study Schr\"odinger operators on $\R$ with measures as potentials.
  Choosing a suitable subset of measures we can work with a dynamical system
consisting of measures. We then relate properties of this dynamical system with
spectral properties of the associated operators.
  The constant spectrum in the strictly ergodic case coincides with the union
of the zeros of the Lyapunov exponent and the set of non-uniformities of the
transfer matrices.
  This result enables us to prove Cantor spectra of zero Lebesgue measure for a
large class of operator families, including many operator families generated by
aperiodic subshifts.

31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin