Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Genericity of non-uniform hyperbolicity in dimension 3   For a generic conservative diffeomorphism of a 3-manifold M, the Oseledets
splitting is a globally dominated splitting. Moreover, either all Lyapunov
exponents vanish almost everywhere, or else the system is non-uniformly
hyperbolic and ergodic. This is the 3-dimensional version of a well-known
result by Ma\~n\'e-Bochi, stating that a generic conservative surface
diffeomorphism is either Anosov or all Lyapunov exponents vanish almost
everywhere. This result inspired and answers in the positive for dimension 3 a
conjecture by Avila and Bochi. We also prove that all partially hyperbolic sets
with positive measure and center dimension one have a strong homoclinic
intersection. This implies that Cr generically for any r, a diffeomorphism
contains no proper partially hyperbolic sets with positive measure and center
dimension one.

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The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
1
The categories of this paper are: cs
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The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
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The categories of this paper are: atom-ph