Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the spectral Hausdorff dimension of 1D discrete Schr\"odinger
  operators under power decaying perturbations   We show that spectral Hausdorff dimensional properties of discrete
Schr\"oodinger operators with (1) Sturmian potentials of bounded density and
(2) a class of sparse potentials are preserved under suitable polynomial
decaying perturbations, when the spectrum of these perturbed operators have
some singular continuous component.

28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph