Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Herman's Theory Revisited   We prove that a $C^{2+\alpha}$-smooth orientation-preserving circle
diffeomorphism with rotation number in Diophantine class $D_\delta$,
$0<\delta<\alpha\le1$, is $C^{1+\alpha-\delta}$-smoothly conjugate to a rigid
rotation. We also derive the most precise version of Denjoy's inequality for
such diffeomorphisms.

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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
3
The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg