Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Resonances in Loewner equations   We prove that given a Herglotz vector field on the unit ball of
$\mathbb{C}^n$ of the form $H(z,t)=(a_1 z_1,...,a_n z_n)+O(|z|^2)$ with $\Re
a_j<0$ for all $j$, its evolution family admits an associated Loewner chain,
which is normal if no real resonances occur. Hence the Loewner-Kufarev PDE
admits a solution defined for all positive times.

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The categories of this paper are: hep-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin