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DCDS-B

In this paper we consider $C^{0}$ random perturbations of a
hyperbolic set of a flow. We show that the hyperbolic set is
structurally semi-stable under such perturbations.

DCDS

In this note we
show that, for a class of partially hyperbolic $C^r$ ($r \geq 1$) diffeomorphisms,
(1) Shub's entropy conjecture holds true; (2)
SRB measures exist as zero-noise limits.

DCDS

In this paper, we study the existence of SRB measures for infinite dimensional dynamical systems in a Banach space. We show that if the system has a partially hyperbolic attractor with nontrivial finite dimensional unstable directions, then it has an SRB measure.

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