Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Berger And Turaev's Proof of Herman's Conjecture of Positive Entropy   We present the proof of Berger and Turaev of Herman's positive entropy
conjecture. In every neighbourhood of identity in the set of smooth symplectic
diffeomorphisms of the 2-dimensional disc, there exists a diffeomorphism with
positive metric entropy.

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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc