Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multifractal analysis of the Birkhoff sums of Saint-Petersburg potential   Let $((0,1], T)$ be the doubling map in the unit interval and $\varphi$ be
the Saint-Petersburg potential, defined by $\varphi(x)=2^n$ if $x\in (2^{-n-1},
2^{-n}]$ for all $n\geq 0$. We consider the asymptotic properties of the
Birkhoff sum $S\_n(x)=\varphi(x)+\cdots+\varphi(T^{n-1}(x))$. With respect to
the Lebesgue measure, the Saint-Petersburg potential is not integrable and it
is known that $\frac{1}{n\log n}S\_n(x)$ converges to $\frac{1}{\log 2}$ in
probability. We determine the Hausdorff dimension of the level set $\{x:
\lim\_{n\to\infty}S\_n(x)/n=\alpha\} \ (\alpha>0)$, as well as that of the set
$\{x: \lim\_{n\to\infty}S\_n(x)/\Psi(n)=\alpha\} \ (\alpha>0)$, when
$\Psi(n)=n\log n, n^a $ or $2^{n^\gamma}$ for $a>1$, $\gamma>0$. The fast
increasing Birkhoff sum of the potential function $x\mapsto 1/x$ is also
studied.

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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: cs
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: dg-ga