Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Atomic disintegrations for partially hyperbolic diffeomorphisms   Shub & Wilkinson and Ruelle & Wilkinson studied a class of volume preserving
diffeomorphisms on the three dimensional torus that are stably ergodic. The
diffeomorphisms are partially hyperbolic and admit an invariant central
foliation of circles. The foliation is not absolutely continuous, in fact,
Ruelle & Wilkinson established that the disintegration of volume along central
leaves is atomic. We show that in such a class of volume preserving
diffeomorphisms the disintegration of volume along central leaves is a single
delta measure. We also formulate a general result for conservative three
dimensional skew product like diffeomorphisms on circle bundles, providing
conditions for delta measures as disintegrations of the smooth invariant
measure.

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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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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: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex