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### Open Access Journals

DCDS

Let $M$ be the unit tangent bundle of a compact manifold
with negative sectional
curvatures and let $\hat M$ be a $\mathbb Z^d$ cover for
$M$. Let $\mu$ be the measure of maximal entropy for
the associated geodesic
flow on $M$ and let $\hat\mu$ be the lift of $\mu$ to
$\hat M$.

We show that the foliation $\hat{M^{s s}}$ is ergodic with respect to $\hat\mu$. (This was proved in the special case of surfaces by Babillot and Ledrappier by a different method.) Our method extends to certain Anosov and hyperbolic flows.

We show that the foliation $\hat{M^{s s}}$ is ergodic with respect to $\hat\mu$. (This was proved in the special case of surfaces by Babillot and Ledrappier by a different method.) Our method extends to certain Anosov and hyperbolic flows.

DCDS

In this note we consider measures supported on limit sets of systems that contract on average.
In particular, we present an upper bound on their Hausdorff dimension.

JMD

We establish stable ergodicity of diffeomorphisms with partially
hyperbolic attractors whose Lyapunov exponents along the central direction
are all negative with respect to invariant SRB-measures.

keywords:
Partial hyperbolicity
,
stable ergodicity
,
accessibility
,
Lyapunov exponents
,
SRB-measures.

DCDS

In this paper we give a generalization of Bowen's equidistribution
result for closed geodesics on negatively curved manifolds to rank
one manifolds.

DCDS

We consider the partial analogue of the usual measurable
Livsic theorem for Anosov diffeomorphims in the context of
non-uniformly hyperbolic diffeomorphisms (Theorem 2). Our main
application of this theorem is to the density of absolutely
continuous measures (Theorem 1).

DCDS

none

DCDS

In this paper we show ergodicity of the strong stable foliations for nilpotent
extensions of transitive Anosov flows with respect to the lift of the Gibbs measure for any
Hölder continuous function.

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