 97155 A.Katok, A.Kononenko
 Cocycles' stability for partially hyperbolic systems
(54K, Latex 2e)
Apr 1, 97

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Abstract. In this paper we establish Livshitztype theorems for partially
hyperbolic
systems. To be more precise, we prove that for a large class of
partially
hyperbolic transformations and flows the subspace of Hoelder
coboundaries is
closed and can be described by some natural geometric conditions. This
class
includes an open, in $C^2$ topology, neighborhood of the timeone
maps of contact Anosov flows (for example, the geodesic flows on
manifolds of negative
curvature).
Along the way we prove several results on the transitivity of the pair
of
stable and unstable foliations for partially hyperbolic systems. In
particular,
we establish the transitivity property for the timeone maps of contact
Anosow
flows and their small perturbations, which has important applications to
the
stable ergodicity of the timeone maps of geodesic flows on the
manifolds of
negative curvature.
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97155.tex