Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rigidity for partially hyperbolic diffeomorphisms   In this work we completely classify $C^\infty$ conjugacy for conservative
partially hyperbolic diffeomorphisms homotopic to a linear Anosov automorphism
on the 3-torus by its center foliation behavior. We prove that the uniform
version of absolute continuity for the center foliation is the natural
hypothesis to obtain $C^\infty$ conjugacy to its linear Anosov automorphism. On
a recent work Avila, Viana and Wilkinson proved that for a perturbation in the
volume preserving case of the time-one map of an Anosov flow absolute
continuity of the center foliation implies smooth rigidity. The absolute
version of absolute continuity is the appropriate sceneario for our context
since it is not possible to obtain an analogous result of Avila, Viana and
Wilkinson for our class of maps, for absolute continuity alone fails miserably
to imply smooth rigidity for our class of maps. Our theorem is a global
rigidity result as we do not assume the diffeomorphism to be at some distance
from the linear Anosov automorphism. We also do not assume ergodicity. In
particular a metric condition on the center foliation implies ergodicity and
$C^\infty$ center foliation.

12
The categories of this paper are: nucl-th
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The categories of this paper are: econ
3
The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an