Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Universal hierarchical structure of quasiperiodic eigenfunctions   We determine exact exponential asymptotics of eigenfunctions and of
corresponding transfer matrices of the almost Mathieu operators for all
frequencies in the localization regime. This uncovers a universal structure in
their behavior, governed by the continued fraction expansion of the frequency,
explaining some predictions in physics literature.
  In addition it proves the arithmetic version of the frequency transition
conjecture. Finally, it leads to an explicit description of several
non-regularity phenomena in the corresponding non-uniformly hyperbolic
cocycles, which is also of interest as both the first natural example of some
of those phenomena and, more generally, the first non-artificial model where
non-regularity can be explicitly studied.

3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
1
The categories of this paper are: cs