Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A pasting lemma and some applications for conservative systems   We prove that in a compact manifold of dimension $n\geq 2$, a $C^{1+\alpha}$
volume-preserving diffeomorphisms that are robustly transitive in the
$C^1$-topology have a dominated splitting. Also we prove that for 3-dimensional
compact manifolds, an isolated robustly transitive invariant set for a
divergence-free vector field can not have a singularity. In particular, we
prove that robustly transitive divergence-free vector fields in 3-dimensional
manifolds are Anosov. For this, we prove some ``pasting'' lemma, which allows
to make perturbations in conservative systems.

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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: quant-ph