Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Selfsimilarity and growth in Birkhoff sums for the golden rotation   We study Birkhoff sums S(k,a) = g(a)+g(2a)+...+g(ka) at the golden mean
rotation number a with periodic continued fraction approximations p(n)/q(n),
where g(x) = log(2-2 cos(2 pi x). The summation of such quantities with
logarithmic singularity is motivated by critical KAM phenomena. We relate the
boundedness of log- averaged Birkhoff sums S(k,a)/log(k) and the convergence of
S(q(n),a) with the existence of an experimentally established limit function
f(x) = lim S([x q(n)])(p(n+1)/q(n+1))-S([x q(n)])(p(n)/q(n)) for n to infinity
on the interval [0,1]. The function f satisfies a functional equation f(ax) +
(1-a) f(x)= b(x) with a monotone function b. The limit lim S(q(n),a) for n
going to infinity can be expressed in terms of the function f.

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The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn