Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonuniform Center Bunching and the Genericity of Ergodicity among $C^1$
  Partially Hyperbolic Symplectomorphisms   We introduce the notion of nonuniform center bunching for partially
hyperbolic diffeomorphims, and extend previous results by Burns--Wilkinson and
Avila--Santamaria--Viana. Combining this new technique with other
constructions, we prove that $C^1$-generic partially hyperbolic
symplectomorphisms are ergodic. We also construct new examples of stably
ergodic partially hyperbolic diffeomorphisms.

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The categories of this paper are: q-bio
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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: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph