Preprint A31/2001
Statistical stability for robust classes of maps with non-uniform expansion

Marcelo Viana | Alves, JosÃ© F.

**Keywords: **
SRB measure | statistical stability | non-uniform hyperbolicity

We consider open sets of transformations in a manifold $M$,
exhibiting non-uniformly expanding behaviour in some forward
invariant domain $U\subset M$.
Assuming that each transformation has a unique SRB measure
in $U$, and some general uniformity conditions, we prove
that the SRB measure varies continuously with the dynamics
in the $L^1$-norm.
As an application we show that an open class of maps
introduced in \cite{V} fits this situation, thus proving that
the SRB measures constructed in \cite{A} vary continuously with
the map.