Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Multifractal Spectra of V-Statistics   Let $(X, T)$ be a topological dynamical system and let $\Phi: X^r \to
\mathbb{R}$ be a continuous function on the product space $X^r= X\times ...
\times X$ ($r\ge 1$). We are interested in the limit of V-statistics taking
$\Phi$ as kernel: [\lim_{n\to \infty} n^{-r}\sum_{1\le i_1, ..., i_r\le n}
\Phi(T^{i_1}x, ..., T^{i_r} x).] The multifractal spectrum of topological
entropy of the above limit is expressed by a variational principle when the
system satisfies the specification property. Unlike the classical case ($r=1$)
where the spectrum is an analytic function when $\Phi$ is H\"{o}lder
continuous, the spectrum of the limit of higher order V-statistics ($r\ge 2$)
may be discontinuous even for very nice kernel $\Phi$.

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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
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The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
11
The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci